Inverse Functions

Inverse Functions

​Dr. Tom Giles

Multiple Choice

What is the definition of a function?

• Has inputs and outputs

• Inputs have different outputs every time

• x-values and

  y-values

• Every input has only one output

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function

Multiple Choice

What is f(g(3))?

• 1/8

• 8

• 1/4

• 1/2

You can see how the original input a, produces b through f(x). THEN, b is used as the input to f^-1(x) to BACK to a.

​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)

Subject | Subject

Some text here about the topic of discussion

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

Said another way...

• x's are inputs

• f(x) are the corresponding outputs

• So...f^-1(x) can take the outputs and reproduce the corresponding inputs

• Inverse functions take you back to where you started.

Multiple Choice

What does an inverse function do?

• Nothing

• Makes it bigger

• Does the opposite of the original 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)

Subject | Subject

Some text here about the topic of discussion

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

​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)

Subject | Subject

Some text here about the topic of discussion

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

Multiple Choice

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

• f ^-1(x)
• f ²(x)
• f '(x)
• f ⁺(x)

Multiple Choice

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

• (1, 4) and (4, 6)
• (-4, -1) and (-6, -4)
• (-1, -4) and (-4, -6)
• (4, 1) and (6, 4)

Multiple Choice

Determine f^-1(2) given the following information about an invertible function, f(x)
f(1) = -3
f(2) = -2
f(-1) = 2
f(3) = -1

• 1
• -1
• 2
• -2

Multiple Choice

Given f(x) = x+3, find f^-1(-2).

• -1
• 1
• 5
• -5

Multiple Choice

The inverse has been reflected over which line?

• y = x
• y =1
• y = 0
• y = x + 1

Multiple Choice

Are these functions inverses?

• Yes
• No

Multiple Choice

What is the inverse of the given coordinates: (-2, 2) (3, 0) (7, 7)

• (2, 2) (7, 7) (3, 0)

• (-2, 2) (3, 0) (7, 7)

• (2, -2) (-3, 0) (7, 7)

• (7, 7) (0, 3) (2, -2)

Fill in the Blanks

Fill in the Blanks

Multiple Choice

Find the inverse of $$f\left(x\right)=\sqrt{x}+8$$  

• $$f^{-1}\left(x\right)=x^2+8$$  

• $$f^{-1}\left(x\right)=x^2-8$$  

• $$f^{-1}\left(x\right)=\left(x+8\right)^2$$  

• $$f^{-1}\left(x\right)=\left(x-8\right)^2$$  

Multiple Choice

Find the inverse of $$f\left(x\right)=-\frac{3}{4}x+5$$  

• $$f^{-1}\left(x\right)=5\left(x-\frac{4}{3}\right)$$  

• $$f^{-1}\left(x\right)=-\frac{3}{4}\left(x-5\right)$$  

• $$f^{-1}\left(x\right)=-\frac{4}{3}\left(x-5\right)$$  

• $$f^{-1}\left(x\right)=-5\left(x-\frac{3}{4}\right)$$  

Multiple Choice

Find the inverse of $$f\left(x\right)=3x+2$$  

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

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

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

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