Square Root Functions Lesson

7 Slides • 4 Questions

1

Square Root Functions

2

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.

3

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.

4

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

5

6

Multiple Choice

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

1

2

3

4

7

Multiple Choice

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

1

2

3

4

8

Let's review finding an inverse algebraically.

Step 1. Switch x and y.

Step 2. Solve for y.

9

Let's review finding an inverse algebraically.

Step 1. Switch x and y.

Step 2. Solve for y.

10

Multiple Choice

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

1

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

2

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

3

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

4

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

11

Multiple Choice

Find the inverse of

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

1

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

2

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

3

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

4

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

Square Root Functions

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