# Inverse functions

## Everything You Need in One PlaceHomework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered. | ## Learn and Practice With EaseOur proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals. | ## Instant and Unlimited HelpOur personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now! |

#### Make math click 🤔 and get better grades! 💯Join for Free

0/1

##### Intros

0/7

##### Examples

###### Lessons

**Graph an inverse**

Given the graph of $y = f\left( x \right)$ as shown,

- Sketch the graph of the inverse $y = {f^{ - 1}}\left( x \right)$
in 2 ways:

i) by reflecting $f\left( x \right)$ in the line $y = x$

ii) by switching the x and y coordinates for each point on $f\left( x \right)$ - Is $f\left( x \right)$ a function?

Is ${f^{ - 1}}\left( x \right)$ a function?

- Sketch the graph of the inverse $y = {f^{ - 1}}\left( x \right)$
in 2 ways:
**Inverse of a Quadratic Function**

Consider the quadratic function: $f(x) = (x+4)^2 + 2$- Graph the function $f\left( x \right)$ and state the domain and range.
- Graph the inverse ${f^{ - 1}}\left( x \right)$ and state the domain and range.
- Is ${f^{ - 1}}\left( x \right)$ a function?

If not, describe how to restrict the domain of $f\left( x \right)$ so that the inverse of $f\left( x \right)$ can be a function.

**Determine the equation of the inverse.**

Algebraically determine the equation of the inverse ${f^{ - 1}}\left( x \right)$, given: