3. Functions

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

Find $(\text{ƒ}\circ g)\left(2\right)$.

Find the inverse of each function that is one-to-one. {(1, -3), (2, -7), (4, -3), (5, -5)}

Determine whether each function graphed or defined is one-to-one. y = -√(100 - x²)

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

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

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) = (2x +1)/(x-3)

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=2-x

Determine whether the given functions are inverses.

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

Find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)

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

Find (g∘ƒ)(3).

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

Find the domain of each function. f(x) = √(5x+35)

In Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range off and ƒ¯¹. f(x) = (x+2)³

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

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

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

$(\text{ƒ}\circ \text{ƒ})\left(2\right)$