Question

If f(x)=x+4 and g(x)=x2-1 what is (gof)(x)?

Answer 1

x^2+8x+15

Explanation:

This is g(f(x)), or g(x+4). x+4 squared is x^2+8x+16, and taking 1 away from that is x^2+8x+15.

Answer 2

For this case, we must compose functions.

`f (x) = x + 4\\g (x) = x ^ 2-1`

They ask us:
`(g_ {o} f) (x)`

The composite function of f with g.

`(g_ {o} f) (x) = g (f (x)) = (x + 4) ^ 2-1`

By definition we have:

`(a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2`

So:

`(x + 4) ^ 2 = x ^ 2 + 2 (x) (4) + 4 ^ 2 = x ^ 2 + 8x + 16\\(g_ {o} f) (x) = x ^ 2 + 8x + 16-1 = x ^ 2 + 8x + 15`

Answer:

`(g_ {o} f) (x) = x ^ 2 + 8x + 15`