# 1.10 Inverse relations and functions

## Interactive practice questions

Consider the graph of each function below and determine if it has an inverse function.

a

Has an inverse function.

A

Does not have an inverse function.

B

Has an inverse function.

A

Does not have an inverse function.

B
b

Has an inverse function.

A

Does not have an inverse function.

B

Has an inverse function.

A

Does not have an inverse function.

B
Easy
Less than a minute

For each function graphed below, determine if it has an inverse function.

Do the following graphs have inverse functions?

A function is defined as $f\left(x\right)=\frac{x}{8}+3$f(x)=x8+3.

Determine an expression for the inverse function.

### Outcomes

#### MGSE9-12.F.BF.4

Find inverse functions.

#### MGSE9-12.F.BF.4a

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2(x^3) or f(x) = (x+1)/(x-1) for x â‰ 1.

#### MGSE9-12.F.BF.4b

Verify by composition that one function is the inverse of another.

#### MGSE9-12.F.BF.4c

Read values of an inverse function from a graph or a table, given that the function has an inverse.