# Inverse functions

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##### Intros

###### Lessons

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##### 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:

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###### Topic Notes

An inverse function is a function that reverses all the operations of another function. Therefore, an inverse function has all the points of another function, except that the x and y values are reversed.

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