Inverse Functions & Compositions

What does an inverse function do?

• Nothing

• Makes it bigger

• Does the opposite of the original function

What are you supposed to do Algebraically to verify that the two functions f(x) & g(x) are inverses of each other?

• Verify the f(g(x)) = x only

• Verify that g(f(x)) = x only

• Verify that BOTH f(g(x)) = x & g(f(x)) = x

• 5

• 9

• 14

• 21

• -5

• -1

• 0

• 21

Determine whether g(x)=3x-6 and f(x)=1/3x+2 are inverses.

• yes

• no

g(x)=3x+4
h(x)=3x-1
Find g(h(x))

• -9x+11
• 4x²+4x
• 9x+1
• 9x+11

• 2

• -2

• cannot be found

Given that f(x) = 3x + 5 and g(x) = 1/3x + 5, find f(g(x)).  Are the two functions inverses of each other?

• x + 20 ; Yes they are inverses
• x + 20 ; No, they are not inverses
• x ; Yes they are inverses
• x ; No, they are not inverses

f(x) = 3x + 10

g(x) = ⅓x - 3

Find g(f(x))

• f(g(x)) = 1

• f(g(x)) = x

• f(g(x)) = 0

• None of these.