Algerbra question

Question

For the functions f(x) = x2 + 4 and g(x) = x2 + 1, find the composite function (f ∘ g)(x).

Answer 1

the composite function that you want to use here is (f o g)(x) = f(g(x))

for this set of functions that means that you substitute in the entire function g(x) into the function f(x)

f(x^2 + 1) = (x^2 + 1)^2 + 4

=x^4 + 2x^2 + 1 + 4

=x^4 + 2x^2 + 5

Answer 2

f(x)=x² +4, g(x) = x² +1

 

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

              =f(x² +1)

              =(x²+1)² +4

              =x⁴ +2x² +1 +4

              =x⁴ +2x² +5