Operations on Functions, Composition of Functions, and Solve Inverses Review

Operations on Functions

100

f(x)=x²-18x+80

g(x)=x-10

Find: (f+g)(x)

x²-17x+70

200

f(x)=x²-5x-36

g(x)=x-9

Find: (f-g)(x)

x²-6x-27

300

f(x)=x²+6x-16

g(x)=x+8

Find:(f·g)(x)

x³+14x²+32x-128

400

f(x)=x²-16x+60

g(x)=x-10

Find: (f/g)(x)

x-6

500

f(x)=6x²+11x+4

g(x)=2x+1

Find: (f/g)(x)

3x+4

Composition of Functions

100

f(x)=x-4

g(x)=3x²+6x+9

Find: (f∘g)(x)

3x²+6x+5

200

f(x)=-x-5

g(x)=x²-6x+13

Find: (f∘g)(x)

-x²+6x-18

300

f(x)=x²+x+8

g(x)=3x+5

Find: f(g(x))

9x²+33x+38

400

f(x)=2x²-4x-6

g(x)=2x+7

Find: f(g(x))

8x²+48x+64

500

f(x)=2x²-5x-12

g(x)-2x+2

Find: (f∘g)(x)

8x²-6x-14

Solve Inverse Functions

100

f(x)=6(x-3)

Find: f^-1(x)

f^-1(x)=x/6 +3

200

f(x)=√ x+2

Find: f^-1(x)

f^-1(x)=x²-2

300

f(x)=(x-10)/9

Find: f^-1(x)

f^-1(x)=9x+10

400

f(x)=⁵√x+2

Find: f^-1(x)

f^-1(x)=x⁵-2

500

f(x)=x³+6

Find: f^-1(x)

f^-1(x)=³√x-6

Verify Inverse Functions

500

Are the two functions inverses?

f(x)=3x-7 

g(x)=4x² - 5

What is g(f(x))?

No!