3. Functions

Given the functions $h\left(x\right)=2x^3-4$ and $k\left(x\right)=x^2+2$, find and fully simplify $h\cdot k\left(x\right)$

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

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)