Question

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

Part 1):

• 
  `f(g(6))=19`

Part 2):

• 
  `g(f(-7))=-34`

Part 3):

• 
  `f(f(8))=224`

Part 4):

• 
  `g(f(x))=5x+1`

Explanation:

Considering the function

`f(x) = 5x + 4`

`g(x) = x - 3`

Part 1)

To evaluate
`f(g(6))`, you must find
`g(6)`

so

`g(x) = x - 3`

Put x = 6

`g(6) = 6 - 3`

`g(6) = 3`

Then

`f(g(6))=f(3)`

`=5(3)+4`

`=19`

Therefore,
`f(g(6))=19`

Part 2)

To evaluate
`g(f(-7))`, you must find
`f(-7)`

so

`f(x) = 5x + 4`

Put x = -7

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

`=-35+4`

`=-31`

Then

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

`= (-31) - 3`

`=-34`

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

Part 3)

To evaluate
`f(f(8))`, you must find
`f(8)`

`f(x) = 5x + 4`

Put x = 8

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

Then

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

Therefore,

`f(f(8))=224`

Part 4)

Evaluate

`g(f(x))`

As

`f(x) = 5x + 4`

`g(x) = x - 3`

so

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

`=(5x+4)-3`

`=5x+4-3`

`=5x+1`

Therefore,

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