Quiz 5

Checkpoint Quiz 5.1

Name:

1. Let f (x) =
√

x − 2 and g(x) =
x2

x2 − 1
.

(a) Find the domain of f ◦ g and find and simplify a formula for (f ◦ g) (x).

(b) Find the domain of g ◦ f and find and simplify a formula for (g ◦ f ) (x).

2. Write F (x) =
√

7x + 5 as a composition of two or more non-identity functions.

Checkpoint Quiz 5.2

Name:

1. Let f (x) =
3x

x + 1
.

(a) Assuming f is one-to-one, find a formula for f−1(x).

(b) Check your answer to part (a) using function composition.

(c) Find the range of f .

2. Explain why a function with more than one x-intercept cannot be invertible.

Checkpoint Quiz 5.3

Name:

1. Solve: x4/3 ≤ 12 − x2/3

2. Let f (x) =
√

5 − x. Find the domain of f ◦ f .