3. Functions

The 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)³

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

$\text{ƒ}\left(x\right)=\frac{2}{x},g\left(x\right)=x+1$

For the pair of functions defined, find (ƒg)(x). Give the domain of each. See Example 2.

ƒ(x)=2x^2-3x, g(x)=x^2-x+3

Determine whether each function graphed or defined is one-to-one. y = 5|x+2|

Let $\text{ƒ}\left(x\right)=x^2+3$ and $g\left(x\right)=-2x+6$. Find each of the following. See Example 1.

$(\text{ƒ}+g)(-5)$

Determine whether each function graphed or defined is one-to-one.

Without using paper and pencil, evaluate each expression given the following functions. $\text{ƒ}\left(x\right)=x+1$ and $g\left(x\right)=x^2$

$(g\circ \text{ƒ})\left(2\right)$

The 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

Given functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. ƒ(x)=√(x-2), g(x)=2x

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

Exercises 123–125 will help you prepare for the material covered in the next section. Solve for y: x = y² -1, y ≥ 0.

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

(ƒg)(1)

The 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 - 3

The 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 +3

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒ-g)(-1)