Question

Someone please help me answer these!

Answer 1

Answer:

$f(8) = 81$

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

Step-by-step 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:

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