Composite functions

The Maths Habit

Start with 5.
Double it, then add 3.
Or add 3, then double it.
Does the order matter?

Yes: 13 or 16

Work out

  1. g(4) when g(x) = x + 3

    7

  2. f(7) when f(x) = 2x + 1

    15

  3. h(−3) when h(x) = x2

    9

  4. k(10) when k(x) = x2 − 1

    4

Composite function
Two functions used one after the other.

Which function goes first?

  1. fg(5)

    g

  2. gf(5)

    f

  3. fg(x)

    g

  4. gf(−2)

    f

f(x) = x + 4 and g(x) = 2x

3× 2g6+ 4f10

fg(3): g goes first

fg(3) = 10

f(x) = x + 4 and g(x) = 2x

3+ 4f7× 2g14

gf(3): f goes first

gf(3) = 14

The order matters.

The quick way to write it

fg(3): the letter next to the bracket goes first

g(3) = 6

f(6) = 10

f(x) = 3x and g(x) = x + 2. Find fg(5).

the letter next to the bracket goes first
g(5) =7
f(7) =21
Answer21

f(x) = x2 and g(x) = x − 4. Find fg(6).

the letter next to the bracket goes first
g(6) =2
f(2) =4
Answer4

f(x) = 3x and g(x) = x + 2. Find fg(5).

the letter next to the bracket goes first
g(5) =7
f(7) =21
Answer21

f(x) = 2x − 1 and g(x) = 5x. Find gf(3).

the letter next to the bracket goes first
f(3) =5
g(5) =25
Answer25

Composite functions worksheet, page 1

Answer sheet

  1. f(x) = 2x + 3. Find ff(1).

    13

  2. f(x) = 5x − 2 and g(x) = x + 4. Find fg(x) in its simplest form.

    5(x + 4) − 2 = 5x + 18

  3. f(x) = x + 2 and g(x) = 3x. Solve fg(x) = 14.

    x = 4

  1. f(x) = 4x and g(x) = x − 3. Find fg(5).

    8

  2. f(x) = x2 and g(x) = 2x + 1. Find gf(3).

    19

  3. f(x) = 2x − 5 and g(x) = x + 4. Find fg(x). Give your answer in its simplest form.

    2x + 3
Exit tickets to print