3. Functions

Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒ+g)(2)

Multiple Choice

Given the functions $L\left(x\right)=x-2$ and $M\left(x\right)=x^2$ , calculate $\frac{L}{M}\left(5\right)$

177

Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒ/g)(2)

205

In Exercises 1–30, find the domain of each function. f(x) = x² - 2x - 15

243

Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ+g)(3)

208

Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ-g)(-1)

In Exercises 1–30, find the domain of each function. f(x) = 1/[3/(x - 1) - 2]

235

Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ/g)(-1)

236

For the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-8

220

For the pair of functions defined, find (ƒ+g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-5

223

For 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+3

223

For the pair of functions defined, find (ƒ+g)(x). Give the domain of each. See Example 2. ƒ(x)=√(4x-1), g(x)=1/x

307

In Exercises 1–30, find the domain of each function. h(x) = √(x −2)+ √(x +3)

In Exercises 31–50, find fg and determine the domain for each function. f(x) = x -5, g(x) = 3x²

413

Use the graph to evaluate each expression. See Example 3(a). (ƒ+g)(2)

217

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

243

Use the graph to evaluate each expression. See Example 3(a). (ƒ-g)(-1)

185

In Exercises 31–50, find ƒ/g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1

In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1

196

In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 15

268

In Exercises 31–50, find fg and determine the domain for each function. f(x) = √x, g(x) = x − 4

215

In Exercises 31–50, find f/g and determine the domain for each function. f(x) = 2 + 1/x, g(x) = 1/x

194

For 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-x

210

In Exercises 31–50, find fg and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)

201

In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)

201

For 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

In 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)

210

For 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

186

For 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+2x^2

214

In Exercises 51–66, find a. (fog) (x) b. (go f) (x) f(x)=4x-3, g(x) = 5x² - 2

224

For 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^2-4x+2

211

In Exercises 51–66, find a. (fog) (2) b. (go f) (2) f(x) = 4-x, g(x) = 2x² +x+5

228

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (g∘ƒ)(0)

245

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (g∘g)(-2)

In Exercises 51–66, find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2). f(x) = 1/x, g(x)= 1/x

219

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=8x+12, g(x)=3x-1

284

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=√x, g(x)=x+3

199

In 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)^4

325

Given 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-1

268

Given 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^2-4

231

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=√(x-1), g(x)=3x

302

Use the graphs of f and g to solve Exercises 83–90.

Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=√x, g(x)=1/(x+5)

171

In Exercises 87–88, find a. (f ○ g)(x); b. the domain of (f ○ g). f(x) = (x + 1)/(x - 2), g(x) = 1/x

290

Use the graphs of f and g to solve Exercises 83–90.

Use the graphs of f and g to solve Exercises 83–90.

Let ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (g ○ ƒ)(x)

189

Let ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (g ○ ƒ)(3)

199

Use the table to evaluate each expression, if possible. (ƒ+g)(1)

240

Solve and check: (x-1)/5 - (x+3)/2 = 1- x/4

231

Use the table to evaluate each expression, if possible. (f/g) (0)

248

The graphs of two functions ƒ and g are shown in the figures.

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ . Determine the domain for each function.

$f\left(x\right)=6x^2-x-1$ , $g\left(x\right)=x-1$

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ . Determine the domain for each function.

$f\left(x\right)=5-x^2$ , $g\left(x\right)=x^2+4x-12$

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ . Determine the domain for each function.

$f\left(x\right)=\sqrt{x}$ , $g\left(x\right)=x-5$

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ . Determine the domain for each function.

$f\left(x\right)=6-\frac{1}{x}$ , $g\left(x\right)=\frac{1}{x}$

In Exercises 82–84, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x) = 3x - 1, g(x) = x - 5

In Exercises 82–84, find f + g, f - g, fg, and f/g. Determine the domain for each function. f(x) = √(x + 7), g(x) = √(x - 2)

Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒg)(4)

In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x)= = (3x+1)/(x² - 25), g(x) = (2x -4)/(x² - 25)

In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x)= = 9x/(x - 4), g(x) = 7/(x+8)