Algebra 2 Composition and Inverse of Functions

Composition

1

f(x) = 3x²

g(x) = x - 2 

Find g(f(x)).

3x² - 2

2

f(x) = x + 1

g(x) = x² + 2

Find f(g(2))

7

3

f(x) = x

g(x) = -x + 5

f(x) + g(x)

5

4

f(x) = 3x - 1 ; g(x) = 2x² + 4

f+g(x)

2x² + 3x - 3

5

f(x) = 3x - 1 ; g(x) = 2x² + 4

g-f(x)

2x² - 3x + 5

Composition

1

f(x) = x + 1

g(x) = x² + 2

Find f(g(0))

3

2

f(x) = x + 1

g(x) = x² + 2

Find g(f(3))

18

3

f(x) = x + 1

g(x) = x² + 2

Find f(f(5))

7

4

f(x) = x + 1

g(x) = x² + 2

Find g(f(5))

38

5

f(x) = 3x²

g(x) = x - 2 

Find g(f(1)).

1

Composition

1

f(x) = 3x

g(x) = x - 2 

Find g+f(x).

4x-2

2

f(x) = 3x²

g(x) = x - 2 

Find g(g(0)).

-4

3

f(x) = 3x²

g(x) = x - 2 

Find g-g(x)

0

4

f(x) = 3x²

g(x) = x - 2 

Find f(g(2)).

0

5

f(x) = 3x²

g(x) = x - 2 

Find f(x)/g(x).

3x + 6 + 12/(x-2)

Inverse

1

Find the inverse. 

 f(x) = 3x - 2

f^-1=(x+2)/3

2

Find the inverse.

g(x) = x²

g^-1(x) = sqrt(x)

3

Find the inverse.

g(x) = sqrt(x - 2)

g^-1(x) = x² + 2

4

What are the three steps to get the inverse of a function?

Change into y = , swap x and y, solve for y

5

When finding the inverse of f(x) = x³ - 27, what does it look like in the second step?

x = y³ - 27

Vocab

1

Define term. 

number and/* a variable