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\(\right\))$

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

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒg)(4)

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)

Find ƒ+g, ƒ- g, ƒg and ƒ/g. Determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1

Find ƒ/g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1

Find the domain of each function. f(x) = 1/[4/(x - 1) - 2]

Find a. (fog) (2) b. (go f) (2) f(x) = 4-x, g(x) = 2x² +x+5

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

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

Graph f+g.

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 and determine the domain for each function. f(x) = 2 + 1/x, g(x) = 1/x

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

Find (g-f) (-2).

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)

Find fg and determine the domain for each function. f(x) = √x, g(x) = x − 4