Inverse Functions Review

How do you determine the steps for an inverse function, if you're starting with the steps for the original function?

Select ALL correct answers.

• Keep the steps in the same order

• Reverse the order of the original steps

• Use the inverse operation in each step (ex: add instead of subtract)

• Use the same operation in each step

What does an inverse function do?

• Nothing

• Makes it bigger

• Reverses the process of the original function

f(x) is a function with the following steps:

1. Multiply by 2

2. Square the quantity

3. Add 9

What is the equation for f(x)?

• $f\left(x\right)=\left(2x+9\right)^2$

• $f\left(x\right)=\left(2x\right)^2+9$

• $f\left(x\right)=2x^2+9$

Select the two expressions which are inverses of each other:

• $x-4$

• $4x$

• $\frac{x}{4}$

• $\frac{4}{x}$

Select the two expressions which are inverses of each other:

• $\sqrt{x+2}$

• $\sqrt{x-2}$
  

• $\left(x+2\right)^2$
  

• $\sqrt{x}-2$
  

Select the option that shows the steps for this function in order: $f\left(x\right)=\frac{\sqrt{x+6}}{3}$  

• 1. Add 6 to x 
  2. Square the quantity 
  3. Divide by 3

• 1. Take the square root of x 
  2. Add 6 
  3. Divide by 3

• 1. Add 6 to x 
  2. Take the square root of the quantity 
  3. Divide by 3

• 1. Square x 
  2. Add 6 
  3. Divide by 3

If $f\left(x\right)=\frac{\sqrt{x+6}}{3}$  , select the correct steps for the INVERSE function in the correct order

• 1. Multiply by 3 

  2. Take the square root of the quantity 
  3. Add 6

• 1. Square x 
  2. Subtract 6 
  3. Multiply by 3

• 1. Subtract 6 
  2. Square the quantity 
  3. Multiply by 3

• 1. Multiply by 3 
  2. Square the quantity 
  3. Subtract 6

Select the option that shows the steps for this function in order: $f\left(x\right)=7\left(x+4\right)^2$  

• 1. Add 4 to x 
  2. Square the quantity 
  3. Multiply by 7

• 1. Square x 
  2. Add 4 
  3. Multiply by 7

• 1. Add 4 to x 
  2. Multiply by 7 
  3. Square the quantity

If $f\left(x\right)=7\left(x+4\right)^2$  , select the correct steps for the INVERSE function in the correct order

• 1. Subtract 4 

  2. Take the square root of the quantity 
  3. Divide by 7

• 1. Divide by 7 
  2. Take the square root of the quantity 
  3. Subtract 4

• 1. Take the square root of x 
  2. Subtract 4 
  3. Divide by 7

If f(x) is a function with the following steps:

1. Add 3

2. Multiply by 5

What is the function?

• f(x) = 5x + 3

• f(x) = 3x + 5

• f(x) = 5(x + 3)

• f(x) = 3(x+5)