Textbook QuestionWithout using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒg)(2)189views
Textbook QuestionWithout using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒ∘g)(2)275views
Textbook QuestionWithout using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (g∘ƒ)(2)371views
Textbook QuestionLet ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ+g)(3)209views
Textbook QuestionIn Exercises 1–30, find the domain of each function. f(x) = 1/(x^2+1) - 1/(x^2-1)258views
Textbook QuestionLet ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒg)(-3)211views
Textbook QuestionLet ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ/g)(-1)236views
Textbook QuestionFor the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-8221views
Textbook QuestionFor the pair of functions defined, find (ƒg)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-7214views
Textbook QuestionFor the pair of functions defined, find (ƒ/g)(x). Give the domain of each. See Example 2. ƒ(x)=2x^2-3x, g(x)=x^2-x+3206views
Textbook QuestionFor the pair of functions defined, find (ƒ-g)(x). Give the domain of each. See Example 2. ƒ(x)=2x^2-3x, g(x)=x^2-x+3224views
Textbook QuestionFor the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2. ƒ(x)=√(4x-1), g(x)=1/x191views
Textbook QuestionFor the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2. ƒ(x)=√(4x-1), g(x)=1/x185views
Textbook QuestionIn Exercises 1–30, find the domain of each function. f(x) = (2x+7)/(x^3 - 5x^2 - 4x+20)266views
Textbook QuestionIn Exercises 31–50, find f/g and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1232views
Textbook QuestionIn Exercises 31–50, find fg and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1234views
Textbook QuestionIn Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1285views
Textbook QuestionIn Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = x -5, g(x) = 3x²221views
Textbook QuestionIn Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1196views
Textbook QuestionIn Exercises 31–50, find fg and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1248views
Textbook QuestionIn Exercises 31–50, find f−g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1253views
Textbook QuestionIn Exercises 31–50, find f/g and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 18277views
Textbook QuestionIn Exercises 31–50, find fg and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 17502views
Textbook QuestionIn Exercises 31–50, find fg and determine the domain for each function. f(x) = √x, g(x) = x − 4215views
Textbook QuestionIn Exercises 31–50, find f−g and determine the domain for each function. f(x) = √x, g(x) = x − 4206views
Textbook QuestionIn Exercises 31–50, find fg and determine the domain for each function. f(x) = 2 + 1/x, g(x) = 1/x212views
Textbook QuestionIn Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 2 + 1/x, g(x) = 1/x215views
Textbook QuestionIn Exercises 31–50, find ƒ+g and determine the domain for each function. f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)194views
Textbook QuestionFor each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=2-x212views
Textbook QuestionIn Exercises 31–50, find f/g and determine the domain for each function. f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)455views
Textbook QuestionIn Exercises 31–50, find fg and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)202views
Textbook QuestionIn Exercises 31–50, find f−g and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)194views
Textbook QuestionIn Exercises 31–50, find f/g and determine the domain for each function. f(x) = √(x +4), g(x) = √(x − 1)203views
Textbook QuestionIn Exercises 31–50, find fg and determine the domain for each function. f(x) = √(x +4), g(x) = √(x − 1)194views
Textbook QuestionFor each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=-2x+5207views
Textbook QuestionIn Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)210views
Textbook QuestionIn Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)282views
Textbook QuestionFor each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=1/x205views
Textbook QuestionIn Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)332views
Textbook QuestionIn Exercises 51–66, find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2). f(x) = 2x, g(x) = x+7193views
Textbook QuestionIn Exercises 51–66, find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2). f(x) = x+4, g(x) = 2x + 1252views
Textbook QuestionFor each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=1-x^2192views
Textbook QuestionFor each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=x^2+3x+1263views
Textbook QuestionIn Exercises 51–66, find a. (fog) (2) b. (go f) (2) f(x)=4x-3, g(x) = 5x² - 2251views
Textbook QuestionIn Exercises 51–66, find a. (fog) (2) b. (go f) (2) f(x) = x²+2, g(x) = x² – 2260views
Textbook QuestionLet ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (ƒ∘g)(-2)216views
Textbook QuestionIn Exercises 51–66, find a. (fog) (2) b. (go f) (2) f(x) = 4-x, g(x) = 2x² +x+5228views
Textbook QuestionIn Exercises 51–66, find a. (fog) (x) b. (go f) (x) f(x) = 4-x, g(x) = 2x² +x+5344views
Textbook QuestionLet ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (g∘ƒ)(0)245views
Textbook QuestionIn Exercises 51–66, find c. (fog) (2) d. (go f) (2). f(x) = √x, g(x) = x − 1280views
Textbook QuestionLet ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (ƒ∘ƒ)(2)275views
Textbook QuestionIn Exercises 51–66, find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2). f(x) = 2x-3, g(x) = (x+3)/2326views
Textbook QuestionIn Exercises 59-64, let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. g (f[h (1)])271views
Textbook QuestionIn Exercises 59-64, let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. f(g[h (1)])197views
Textbook QuestionIn Exercises 67-74, find a. (fog) (x) b. the domain of f o g. f(x) = √x, g(x) = x − 2243views
Textbook QuestionIn Exercises 67-74, find a. (fog) (x) b. the domain of f o g. f(x) = x² + 4, g(x) = √(1 − x)233views
Textbook QuestionGiven functions f and g, (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=-6x+9, g(x)=5x+7223views
Textbook QuestionGiven functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=8x+12, g(x)=3x-1285views
Textbook QuestionIn Exercises 75-82, express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x). h(x) = (3x − 1)^4325views
Textbook QuestionGiven functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=x^3, g(x)=x^2+3x-1191views
Textbook QuestionGiven functions f and g, (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=x^3, g(x)=x^2+3x-1270views
Textbook QuestionGiven functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=x+2, g(x)=x^4+x^2-4232views
Textbook QuestionGiven functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=√(x-1), g(x)=3x302views
Textbook QuestionGiven functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=√(x-1), g(x)=3x236views
Textbook QuestionIn Exercises 76–81, find the domain of each function. f(x) = x/(x^2 + 4x -21)235views
Textbook QuestionIn Exercises 75-82, express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x). h(x) = 1/(2x-3)469views1rank
Textbook QuestionGiven functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=2/x, g(x)=x+1426views
Textbook QuestionIn Exercises 82–84, find f + g, f - g, fg, and f/g. f(x) = x^2 + x + 1, g(x) = x^2 -1215views
Textbook QuestionGiven functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=√(x+2), g(x)=-(1/x)258views
Textbook QuestionGiven functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=√(x+2), g(x)=-(1/x)227views
Textbook QuestionGiven functions f and g, (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=1/(x-2), g(x)=1/x194views
Textbook QuestionUse the graphs of f and g to solve Exercises 83–90. Find the domain of ƒ + g.371views
Textbook QuestionGiven functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=1/(x-2), g(x)=1/x192views
Textbook QuestionIn Exercises 91–94, use the graphs of f and g to evaluate each composite function. (go f) (0)757views
Textbook QuestionIn Exercises 95–96, find all values of x satisfying the given conditions. f(x) = 2x − 5, g(x) = x² − 3x + 8, and (ƒ o g) (x) = 7.637views
Textbook QuestionLet ƒ(x) = 3x^2 - 4 and g(x) = x^2 - 3x -4. Find each of the following. (f/g)(-1)225views
Textbook QuestionLet ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (g ○ ƒ)(x)189views
Textbook QuestionLet ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (g ○ ƒ)(3)199views
Textbook QuestionLet ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. the domain of ƒ ○ g197views
Textbook QuestionThe functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = (x+2)³48views
Textbook QuestionThe functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = x³ +260views
Textbook QuestionThe functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = 2x + 342views
Textbook QuestionThe functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = 2x44views
Textbook QuestionThe functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = x +371views
Textbook QuestionIn Exercises 1-10, find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = ∛(x − 4) and g(x) = x³ +437views
Textbook QuestionIn Exercises 1-10, find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = = -x and g(x) = -x59views
Textbook QuestionIn Exercises 1-10, find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = 3/(x-4) and g(x) = 3/x + 465views
Textbook QuestionIn Exercises 1-10, find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x)=5x-9 and g(x) = (x+5)/945views
Textbook QuestionIn Exercises 1-10, find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = 4x + 9 and g(x) = (x-9)/448views
Textbook QuestionIn Exercises 1-10, find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = 4x and g(x) = x/446views
Textbook QuestionExercises 123–125 will help you prepare for the material covered in the next section. Solve for y: x = y² -1, y ≥ 0.53views
Textbook QuestionExercises 123–125 will help you prepare for the material covered in the next section. Solve for y : x = 5/y + 445views
Textbook QuestionIn Exercises 59-64, let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. ƒ¹ (1)46views
Textbook QuestionThe functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = (2x +1)/(x-3)37views
Textbook QuestionThe functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = (x +4)/(x-2)43views
Textbook QuestionThe functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = √x75views
Textbook QuestionIn Exercises 101–102, find an equation for f^(-1)(x). Then graph f and f^(-1) in the same rectangular coordinate system. f(x) = 1 - x^2, x ≥ 0.50views
Textbook QuestionWhich graphs in Exercises 96–99 represent functions that have inverse functions?36views
Textbook QuestionThe functions in Exercises 93–95 are all one-to-one. For each function, (a) find an equation for f^(-1)x, the inverse function. (b) Verify that your equation is correct by showing that f(f^(-1)(x)) = x and f^(-1)(f(x)) = x. f(x) = (x - 7)/(x + 2)176views
Textbook QuestionThe functions in Exercises 93–95 are all one-to-one. For each function, (a) find an equation for f^(-1)x, the inverse function. (b) Verify that your equation is correct by showing that f(f^(-1)(x)) = x and f^(-1)(f(x)) = x. f(x) = 4x - 3123views
Textbook QuestionUse a graphing calculator to graph each equation in the standard viewing window. y = 3x + 415views
Textbook QuestionDetermine whether each function graphed or defined is one-to-one. y = -√100 - x^220views
Textbook QuestionDetermine whether each function graphed or defined is one-to-one. y = 2x^3 - 124views
Textbook QuestionDetermine whether each function graphed or defined is one-to-one. y = -1 / x+223views
Textbook QuestionDetermine whether each function graphed or defined is one-to-one. y = x+4 / x-316views
Textbook QuestionDetermine whether each function graphed or defined is one-to-one. y = 2(x+1)^2 - 626views
Textbook QuestionDetermine whether each function graphed or defined is one-to-one. y = ∛x+1 - 326views
Textbook QuestionUse the definition of inverses to determine whether ƒ and g are inverses. f(x) = -4x+2, g(x) = -1/4x - 232views
Textbook QuestionUse the definition of inverses to determine whether ƒ and g are inverses. f(x) = x+1/x-2, g(x) = 2x+1/x-129views
Textbook QuestionUse the definition of inverses to determine whether ƒ and g are inverses. f(x) = 2/x+6, g(x) = 6x+2/x29views
Textbook QuestionUse the definition of inverses to determine whether ƒ and g are inverses. f(x) = x^2+3, x≥0; g(x) = √x-3, x≥323views
Textbook QuestionDetermine whether the given functions are inverses. ƒ= {(2,5), (3,5), (4,5)}; g = {(5,2)}27views
Textbook QuestionFind the inverse of each function that is one-to-one. {(3,-1), (5,0), (0,5), (4, 2/3)}34views
Textbook QuestionFind the inverse of each function that is one-to-one. {(1, -3), (2, -7), (4, -3), (5, -5)}24views
Textbook QuestionIn Exercises 1-10, find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x)=3x+8 and g(x) = (x-8)/321views
Textbook QuestionThe functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f^-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ^-1 (x)) = = x and ƒ^-1 (f(x)) = x. f(x) = 1/x51views
Textbook QuestionWhich graphs in Exercises 29–34 represent functions that have inverse functions?47views
Textbook QuestionWhich graphs in Exercises 29–34 represent functions that have inverse functions?27views
Textbook QuestionWhich graphs in Exercises 29–34 represent functions that have inverse functions?30views
Textbook QuestionIn Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range of f and ƒ¯¹. f(x)=2x-138views
Textbook QuestionIn Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range of f and ƒ¯¹. ƒ(x) = x² − 4, x ≥ 072views
Textbook QuestionIn Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range off and ƒ¯¹. f(x) = (x − 1)², x ≤ 137views
Textbook QuestionIn Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range off and ƒ¯¹. f(x) = x³ − 141views
Textbook QuestionIn Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range off and ƒ¯¹. f(x) = (x+2)³40views
Textbook QuestionIn Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range off and ƒ¯¹. f(x) = √(x-1)44views
Textbook QuestionIn Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range off and ƒ¯¹. f(x) = ∛x + 147views
Multiple ChoiceGiven the functions f(x)=x+4f\left(x\right)=\sqrt{x+4}f(x)=x+4 and g(x)=(x−2)2−4g\left(x\right)=\left(x-2\right)^2-4g(x)=(x−2)2−4 find (f∘g)(x)\left(f\circ g\right)\left(x\right)(f∘g)(x) and (g∘f)(x)\left(g\circ f\right)\left(x\right)(g∘f)(x)200views2rank2comments
Multiple ChoiceGiven the functions f(x)=1x2−2f(x)=\frac{1}{x^2-2}f(x)=x2−21 and g(x)=x+2g(x)=\sqrt{x+2}g(x)=x+2 find (f∘g)(x)(f∘g)(x)(f∘g)(x) and (g∘f)(x)(g\circ f)(x)(g∘f)(x).203views
Multiple ChoiceGiven the functions f(x)=x+3f(x)=x+3f(x)=x+3 and g(x)=x2g(x)= x^2g(x)=x2 find (f∘g)(2)(f∘g)(2)(f∘g)(2) and (g∘f)(2)(g∘f)(2)(g∘f)(2).183views
Multiple ChoiceGiven the functions f(x)=x2f(x) = x^2f(x)=x2 and g(x)=x−8g(x)=\sqrt{x-8}g(x)=x−8 find (f∘g)(x)(f∘g)(x)(f∘g)(x) and determine its domain.185views