Lesson 14

Inverse of Square Root Functions

Lesson 14 TEKS 2A.4C

Let's start with an easy reminder...

•Step1: Let f(x) = y

•Step 2: Interchange x and y

•Step 3: Solve for y

•Step 4: Change y to f^-1(x)

Subject | Subject

Some text here about the topic of discussion

​Find the inverse of the following function: f(x) = x-3

How did you do?

•Step1: Let f(x) = y

•Step 2: Interchange x and y

•Step 3: Solve for y

•Step 4: Change y to f^-1(x)

​Find the inverse of the following function: f(x) = x -3

Match

Match the steps with the correct order.

• Switch the x and the y

• Solve for y

• Set f(x)=y

• Use function notation

Step 2

Step 3

Step 1

Step 4

• Step 2

• Step 3

• Step 1

• Step 4

How do we find the inverse of a square root function?

​4 steps to find inverse function

•Step1: Let f(x) = y

•Step 2: Interchange x and y

•Step 3: Solve for y

•Step 4: Change y to f^-1(x)

​4 steps to find inverse function

•Step1: Let f(x) = y

•Step 2: Interchange x and y

•Step 3: Solve for y

•Step 4: Change y to f^-1(x)

​4 steps to find inverse function

•Step1: Let f(x) = y

•Step 2: Interchange x and y

•Step 3: Solve for y

•Step 4: Change y to f^-1(x)

​4 steps to find inverse function

•Step1: Let f(x) = y

•Step 2: Interchange x and y

•Step 3: Solve for y

•Step 4: Change y to f^-1(x)

Open Ended

What do you notice happens to the equations as you solve for the inverse?

Multiple Choice

Determine the inverse for Example C in your notes:

$$f\left(x\right)=\sqrt[]{x-3}-7$$

• P^-1(x) = $$\frac{\left(x^2-3\right)}{7}$$  

• P^-1(x) = $$\left(x+7\right)^2-3$$  

• P^-1(x) = $$\sqrt[]{\frac{x-7}{3}}$$  

• P^-1(x) = $$\left(x+7\right)^2+3$$  

Multiple Choice

Determine the inverse for Example D in your notes:

$$f\left(x\right)=\sqrt[]{3x+5}$$

• f¯¹(x)= $$\frac{\left(x-5\right)^2}{3}$$

• f¯¹(x)= $$\frac{\left(x^2+5\right)}{3}$$

• f¯¹(x)= $$\frac{\left(x^2-5\right)}{3}$$

• f¯¹(x)= $$\frac{1}{3}x^2-5$$

Multiple Choice

Determine the inverse of the Example E in your notes:

$$f\left(x\right)=6\sqrt[]{x}$$

• f¯¹(x)= $$\left(\frac{x}{6}\right)^2$$

• f¯¹(x)= $$6x^2$$

• f¯¹(x)= $$\frac{x^2}{6}$$

• f¯¹(x)= $$\left(6x\right)^2$$

Let's see the graphs of our functions versus their inverses!

​https://www.desmos.com/calculator/nqmm3dtl36

Poll

Rate your understanding of inverses of square roots! How do you feel?

• I got this in the bag!

• I'm pretty confident.

• Maybe some more practice and I'll be more confident!

• Help...I'm a little lost.