3. Functions

Find the domain of each function. f(x) = 2(x+5)

Find the domain of each function. g(x) = 2/(x+5)

Given functions f and g, find (a)$(\text{ƒ}\circ g)\left(x\right)$ and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=-6x+9,g\left(x\right)=5x+7$

Let $\text{ƒ}\left(x\right)=\text{√}(x-2)$ and $g\left(x\right)=x^2$. Find each of the following, if possible

$\left(g\text{○ƒ}\right)\left(3\right)$

Let $\text{ƒ}\left(x\right)=3x^2-4$ and $g\left(x\right)=x^2-3x-4$. Find each of the following.

$\left(f/g\right)(-1)$

Determine whether each pair of functions graphed are inverses.

Given the functions $f(x)=x+3$ and $g(x)= x^2$ find $(f∘g)(2)$ and $(g∘f)(2)$.

Determine whether each function graphed or defined is one-to-one. y = ∛(x+1) - 3

Use the graph to evaluate each expression. See Example 3(a).

(ƒ/g)(1)

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=x²

Find a. (fog) (2) b. (go f) (2) f(x)=4x-3, g(x) = 5x² - 2

Graph the inverse of each one-to-one function.

Which graphs in Exercises 29–34 represent functions that have inverse functions?

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

$\text{ƒ}\left(x\right)=\surd x,g\left(x\right)=\frac{1}{(x+5)}$

Use the definition of inverses to determine whether ƒ and g are inverses. f(x) = x²+3, x≥0; g(x) = √x-3, x≥3