Inverse Functions

Inverse Functions

Inverse Functions

• An inverse is a function that is used to "undo" another function

• We write inverse functions like:    $f^{-1}\left(x\right)$  

Coordinates

• f(x) has the coordinates (2,9) , (-2,5), and (4, -6)

• The inverse, f^-1(x) has the coordinates (9,2) , (5, -2) and (-6,4)

• notice how the x's and y's switched

• f(x) --> (x,y)

• f^-1(x) --> (y,x)

Graphing

• When we graph the function an the inverse, we see that the inverse if a reflection over the line y=x

• The dotted line on the graph is the line y=x

Multiple Choice

What are the inverse points for the coordinates:

(3, 0) , (2, -4), (5, 5) and (-6,8)

• (3,0) , (2, -4) , (5,5) , (6,8)

• (0,3) , (-4,2) , (5,5) , (8,-6)

• (3,2), (0, -4), (5, -6), (5,8)

Multiple Choice

Are these inverse functions?

• yes

• no

Multiple Choice

Are these functions inverses?

• No

• Yes

• No way to tell

Multiple Choice

Are these functions inverses?

• Yes

• No

Multiple Choice

The inverse has been reflected over which line?

• y = x
• y =1
• y = 0
• y = x + 1

Multiple Choice

Which graph represents the functions f(x) and f^-1(x)?

Finding an Inverse

• Step 1: change f(x) to y

• Step 2: switch x and y

• Step 3: solve for y

• Step 4: change y to f^-1(x)

Multiple Choice

Find the inverse of  $f(x)=10+7x$  

• $f^{-1}(x)=\frac{x-7}{10}$

• $f^{-1}(x)=\frac{x-10}{7}$

• $f^{-1}(x)=\frac{1}{10+7x}$

Multiple Choice

Find the inverse of  $f(x)=4x$  

• $f^{-1}(x)=\frac{x}{4}$

• $f^{-1}(x)=4$

• $f^{-1}\left(x\right)=\frac{1}{4}$

Multiple Choice

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

• $f^{-1}(x)=\frac{3}{5}+x$

• $f^{-1}(x)=3x+5$

• $f^{-1}(x)=5x+3$

Multiple Choice

Find the inverse of  $f(x)=2x+1$  

• $f^{-1}(x)=2x$

• $f^{-1}(x)=\frac{x-1}{2}$

• $f^{-1}(x)=2$

Multiple Choice

Find the inverse of  $f(x)=3x+2$  

• $f^{-1}(x)=3x-2$

• $f^{-1}(x)=2+3x$

• $f^{-1}(x)=\frac{x-2}{3}$

Multiple Choice

The inverse of $f(x)=8x+30$  is  $f^{-1}(x)=\frac{8}{30}$  .

• True

• False

Multiple Choice

The inverse of $f(x)=x+30$   is   $f^{-1}(x)=x-30$  .

• True

• False

• I have no idea how to do this.

Multiple Choice

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

• f ^-1(x)

• f ²(x)

• f '(x)

• f ⁺(x)