Inverses of Square root functions

​Inverses of Square Root Functions

By KATIE KENNEDY

Inverse Operations and AMEG

• The inverse of a square root is an exponent.

• You should remember that because square roots can be written as exponents, the square root is part of the 'e' in the order of solving.

Square root parent function

Drag and Drop

The steps to find the inverse are:

Step 1:​

Placeholder

Step 2:​

Placeholder

Drag these tiles and drop them in the correct blank above

Switch x and y

Solve for y

Add x to y

Multiply x by y

Subtract y from x

Square the x

Change the order of the problem

Multiple Choice

The inverse of the function f(x) is written as ...

• f ^-1(x)
• f ²(x)
• f '(x)
• f ⁺(x)

Math Response

Find the inverse of the square root parent function

$$f\left(x\right)=\sqrt[]{x}$$

make sure to use proper notation

Type answer here

Correct Answer: f^{-1}\left(x\right)=x^2

Deg^°

Rad

Multiple Choice

What is the best description?

• They are both functions, but not inverse functions.

• They are inverse functions.

• They are reflected over y=x, but they are not both functions.

• They are not reflected over y=x, and they are not both functions.

Restricting the domain

Once you have found the inverse, you must find the domain f the inverse by determining which half of the quadratic is not part of the reflection.

​Why the restriction?

Math Response

What should the domain restriction be for the graph of $$f^{-1}\left(x\right)=x^2$$

Type answer here

Correct Answer: x\ge0

Deg^°

Rad

Math Response

Find the inverse function of $$f\left(x\right)=\sqrt{x+11}$$  

Type answer here

Correct Answer: f^{-1}\left(x\right)=x^2-11

Deg^°

Rad

Math Response

What is the domain restriction for the inverse of the square root function $$f\left(x\right)=\sqrt{x+11}$$  

Type answer here

Correct Answer: x\ge0

Deg^°

Rad

Multiple Choice

Find the inverse function of $$f\left(x\right)=\sqrt{x}-6$$  

• $$y=\left(x+6\right)^2$$  

• $$y=\left(x-6\right)^2$$  

• $$y=x^2+6$$  

• $$y=x^2+36$$  

Math Response

What is the domain restriction for the inverse of the square root function

$$f\left(x\right)=\sqrt{x}-6$$  

Type answer here

Correct Answer: x\ge-6

Deg^°

Rad

Math Response

Find the inverse of $$f\left(x\right)=\sqrt{x+2}+9$$  

Type answer here

Correct Answer: f^{-1}\left(x\right)=\left(x-9\right)^2-2

Deg^°

Rad

Math Response

What is the domain restriction for the inverse of the square root function $$f\left(x\right)=\sqrt{x+2}+9$$  

Type answer here

Correct Answer: x\ge-2

Deg^°

Rad

Math Response

Find the inverse function of $$f\left(x\right)=\sqrt{-5x}$$  

Type answer here

Correct Answer: f^{-1}\left(x\right)=-\frac{1}{5}x^2

Deg^°

Rad

Math Response

What is the domain restriction for the inverse of the square root function $$f\left(x\right)=\sqrt{-5x}$$  

Type answer here

Correct Answer: x\ge0

Deg^°

Rad

Math Response

What is the domain restriction for the inverse of the square root function $$f\left(x\right)=-\sqrt{-5x}$$  

Type answer here

Correct Answer: x\le0

Deg^°

Rad