Function Composition and Inverses

What is function composition?

• Plugging one function into another one

• Multiplying two functions

• Adding two functions

• Finding the inverse of a function

Given: $f\left(x\right)=2x-5$  
 $g\left(x\right)=x^2-6x$  
 $h\left(x\right)=2x^2+5x-3$  

Find:  $g\left(f\left(1\right)\right)$  

If f(x) and g(x) are inverses, then f(g(x)) and g(f(x)) are both ______.

•  2(2x² - 1)

• 2(2x)² - 1

• 2x(2x² - 1)

• f2x² - 1

f(x) = 3x + 10

g(x) = x - 2

Find g(0).

• 10

• 4

• -4

• -2

f(x) = 3x + 10
g(x) = x - 2
Find f(g(0))

• 16

• 4

• -4

• 8

If f(x) and g(x) are inverses, then f(g(x)) and g(f(x)) are both ______.

Are these functions inverses?

• Yes
• No

Are the following inverses of each other?

• True
• False

• 2

• 15

• 7

• -9