Square Root Functions

Square Root Functions

Where does a square root function come from?

Look at the quadratic function to the right. To find the inverse, switch the x column with the y column.

There's a slight problem.

This is not a function. We have to restrict the domain to

 $x\ge0$   whichis just the green part of the graph.

Example 1: Find the inverse of the table, graph and restrict the domain.

Multiple Choice

Find the Inverse of the quadratic function show in the table.

Multiple Choice

Find the inverse of the quadratic function show in the graph.

Let's review finding an inverse algebraically.

Step 1. Switch x and y.

Step 2. Solve for y.

Let's review finding an inverse algebraically.

Step 1. Switch x and y.

Step 2. Solve for y.

Multiple Choice

Find the inverse of  $f\left(x\right)\ =\frac{1}{5}x^2$  

•  $f^{-1}\left(x\right)\ =$   $\sqrt{x+5}$  

•  $f^{-1}\left(x\right)\ =$   $\sqrt{5x}$  

•  $f^{-1}\left(x\right)\ =$   $-5x$  

•  $f^{-1}\left(x\right)\ =$   $\sqrt{\frac{1}{5}x}$  

Multiple Choice

Find the inverse of

 $f\left(x\right)\ =\ \sqrt{x\ +\ 1}$  

•  $f^{-1}\left(x\right)\ =\ \left(x+1\right)^2$  

•  $f^{-1}\left(x\right)\ =\ x^2-1$  

•  $f^{-1}\left(x\right)\ =\ 2x+1$  

•  $f^{-1}\left(x\right)\ =\ -x^2$