Question

Someone please help me answer these!

Answer 1

`f(8) = 81`

`(g\ o\ f)(x) = x^2 + 2x -4`

Explanation:

Solving (a):

`f(x) = x^2 + 2x +1`

`g(x) = x - 5`

Solve for f(8)

We have:

`f(x) = x^2 + 2x +1`

Substitute 8 for x

`f(8) = 8^2 + 2*8 +1`

Solve

`f(8) = 64 + 16 +1`

`f(8) = 81`

Solving (b):

`(g\ o\ f)(x)`

This is solved by:

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

So, we have:

`g(x) = x - 5`

`g(f(x)) = f(x) - 5`

Substitute:
`f(x) = x^2 + 2x +1`

`g(f(x)) = x^2 + 2x + 1 - 5`

`g(f(x)) = x^2 + 2x -4`

Hence:

`(g\ o\ f)(x) = x^2 + 2x -4`