Question

For f(x) = x+6 and g(x) = 2x + 3, find the following

a. (fog)(x)
b. (g of)(x)
c. (fog)(2)

Answer 1

`(f o g)(x) = 2x + 9`

`(g o f)(x) = 2x + 15`

`(f o g)(2) = 11`

Explanation:

Given

`f(x) = x+6`

`g(x) = 2x + 3`

Solving (a): (f o g)(x)

In functions:

`(f o g)(x) = f(g(x))`

Solving for f(g(x))

`f(x) = x+6`

`f(g(x)) = 2x + 3 + 6`

`f(g(x)) = 2x + 9`

So:

`(f o g)(x) = 2x + 9`

Solving (a): (g o f)(x)

In functions:

`(g o f)(x) = g(f(x))`

Solving for g(f(x))

`g(x) = 2x + 3`

`g(f(x)) = 2(x+6)+3`

Open bracket

`g(f(x)) = 2x+12+3`

`g(f(x)) = 2x+15`

So:

`(g o f)(x) = 2x + 15`

Solving (c): (f o g)(2)

In (a):

`(f o g)(x) = 2x + 9`

Substitute 2 for x

`(f o g)(2) = 2*2 + 9`

`(f o g)(2) = 4 + 9`

`(f o g)(2) = 11`