Question

Topic : Composition of Functions - Worksheet 2 Using f(x) = 5x + 4 and g(x) = x - 3,find: 1. f(g(6)) 2. g(f(-7)) 3. f(f(8)) 4. g(f(x))

Answer 1

• 
  `f(g(6))=19`

• 
  `g(f(-7))=-34`

• 
  `f(f(8))=224`

• 
  `g(f(x))=5x+1`

Explanation:

Considering the functions

`f(x) = 5x + 4`

`g(x) = x - 3`

Part 1)

Find

• 
  `f(g(6))`

We need to first dertermine
`g(6)`

`g(x) = x - 3`

Putting x = 6

`g(6) = 6-3=3`

Then

`f(g(6))=f(3)=5(3)+4=15+4=19`

Hence,

`f(g(6))=19`

Part 2)

Find

• 
  `g(f(-7))`

We need to first dertermine
`f(-7)`

`f(x) = 5x + 4`

Putting x = -7

`f(-7) = 5(-7)+4=-35+4=-31`

Then

`g(f(-7))=g(-31)=(-31-3)=-34`

Hence,

`g(f(-7))=-34`

Part 3)

Find

• 
  `f(f(8))`

We need to first dertermine
`f(8)`

Putting x = 8

`f(8) = 5(8)+4=40+4=44`

Then

`f(f(8))=f(44)=5(44)+4=220+4=224`

Hence,

`f(f(8))=224`

Part 4)

Find

• 
  `g(f(x))`

`f(x) = 5x + 4`

`g(f(x))=g(5x+4)`

`=(5x+4)-3=5x+1`

Hence,

`g(f(x))=5x+1`