Verifying Inverse Functions

Verify if the two functions are inverses of each other. $f\left(x\right)=-x-5$  

 $g\left(x\right)=-3x-9$  

SHOW YOUR WORK

• Inverse Functions

• Not Inverse Functions

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

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

SHOW YOUR WORK

• yes

• no

 $f(x)=3x+10$  

 $g\left(x\right)=\frac{1}{3}x-3$  
Find  $g(f(x))$  

SHOW YOUR WORK

•  $f(g(x))=1$  
  

•  $f(g(x))=x$  
  

•  $f(g(x))=0$  
  

• None of these.

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

 $f\left(x\right)=4+\frac{1}{3}x$  

 $g\left(x\right)=3x-12$  

SHOW YOUR WORK

• Inverse Functions

• Not Inverse Functions

What operation allows us to verify if functions are inverses?

• Multiplying

• Dividing

• Adding

• Composing

Tags

CCSS.HSF-BF.B.4B

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

• 1

• x

• 0

• y

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

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

SHOW YOUR WORK

• yes

• no

Which of the following relations is a one-to-one function?

• (a)

• (b)

• (c)

• None of these

Which of the following relations is a one-to-one function?

• (a)

• (b)

• (c)

• None of these

The relation in the graph is..

• a function, but not a one-to-one function.

• a one-to-one function.

• not a function