Compositions Of Functions Worksheet With Answer Key printable pdf download

Compositions Of Functions Worksheet With Answer Key

More Compositions of Functions

A composition of functions is just a different way of combining functions. Before, we’ve plugged specific

numbers into functions. In compositions, we plug an entire function into a function.

Example: Let f(x) = 3x + 5 and g(x) = x + 7. Find (f ◦g)(x).

Way #1: (f ◦g)(x) = f(g(x))

Way #2: (f ◦g)(x) = f(g(x))

= f(x + 7)

Because f(____) = 3(____) + 5, then

f( g(x) ) = 3( g(x) ) + 5

f(x + 7) = 3(x + 7) + 5

= 3( x + 7 ) + 5 (Because g(x) = x + 7)

= 3x + 21 + 5

= 3x + 26

So, (f ◦g)(x) = 3x + 26

Use whichever one you find the easiest to work with. Both of them result in the same answer.

Given f(x) = 2x – 7 and g(x) = 2x + 5, find the following:

1) (f ◦g)(x)

2) (g ◦ f)(x)

Given f(x) = 9 – x and g(x) = 5x + 10, find the following:

3) (f ◦g)(x)

4) (g ◦ f)(x)

Given f(x) = x + 6 and g(x) = x

, find the following:

5) (f ◦g)(x)

6) (g ◦ f)(x)

Given f(x) = 4x and g(x) = x

+ 1, find the following:

7) (f ◦g)(x)

8) (g ◦ f)(x)

Answers: 1) 4x + 3

2) 4x – 9

3) -5x – 1

4) -5x + 55

5) x

+ 6

6) x

+ 12x + 36

7) 4x

+ 4

8) 16x

+ 1

Compositions Of Functions Worksheet With Answer Key