Question

f(x)=x^2+3 and g(x)=x^2-4 what is (gof)(x)

Answer 1

For this case we have the following functions:

$f (x) = x ^ 2 + 3\\g (x) = x ^ 2-4$

By definition of composition of functions, we have to:

$(g_ {o} f) (x) = g (f (x))$

So:

$g (f (x)) = (x ^ 2 + 3) ^ 2-4 = (x ^ 2) ^ 2 + 2 (x ^ 2) (3) + 3 ^ 2-4 = x ^ 4 + 6x ^ 2 + 9-4=x^4+6x^2+5$

Thus, we have to:

$(g_ {o} f) (x) = x ^ 4 + 6x ^ 2 + 5$

Answer:

$(g_ {o} f) (x) = x ^ 4 + 6x ^ 2 + 5$