Quiz 9 Inverse Functions

To prove two functions are inverses of each other, both f(g(x)) and g(f(x)) should equal...

• 1

• x

• 0

• y

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

• f ^-1(x)
• f ²(x)
• f '(x)
• f ⁺(x)

When finding the inverse of a relation, 
1st you replace f(x) with y
2nd switch the x's and y's
What do you do next?

• solve for y
• replace y with f^-1(x)
• solve for x
• find the greatest common factor

Determine if $f\left(x\right)$  and  $g\left(x\right)$  are inverses of each other.

 $f\left(x\right)=4+\frac{1}{3}x$  

 $g\left(x\right)=3x-12$  

• Inverse Functions

• Not Inverse Functions

What is the inverse of the points
(1,3)(2,4)(6,8)

• (3,1)(4,2)(8,6)
• (-3,-1)(-4,-2)(-8,-6)
• (1,3)(2,4)(6,8)
• (-1,-3)(-2,-4)(-6,-8)

What's the best description?

• They are both functions, but not 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.

• They are inverse functions.

What's the best description?

• They are both functions, but not 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.

• They are inverse functions.

Is the red graph the inverse of the blue graph?

• no

• yes

• no way to tell

 $f\left(x\right)\ =\ 5x\ -\ 5$   $g\left(x\right)\ =\ \frac{1}{5}x\ +\ 1$  

Use composition of functions to determine if f(x) and g(x) are inverse functions.

• yes inverses 

• no not inverses

Find the inverse of
f(x) = 1/4x - 7

• f^-1(x) = 4x + 7
• f^-1(x) = -4x + 28
• f^-1(x) = -4x - 7
• f^-1(x) = 4x + 28