find (f composed of g)(x)=given f(x)=2x squared +3 g(x)=4x cubed +1
To find the composite function (f∘g)(x), you need to substitute g(x) into f(x).
Given f(x) = 2x^2 + 3 and g(x) = 4x^3 + 1, you can substitute g(x) into f(x) as follows:
(f∘g)(x) = f(g(x))
Replace x in f(x) with g(x):
(f∘g)(x) = 2(g(x))^2 + 3
Now, substitute g(x) = 4x^3 + 1 into the expression:
(f∘g)(x) = 2(4x^3 + 1)^2 + 3
Simplify and expand the expression:
(f∘g)(x) = 2(16x^6 + 8x^3 + 1) + 3
= 32x^6 + 16x^3 + 2 + 3
= 32x^6 + 16x^3 + 5
Therefore, (f∘g)(x) = 32x^6 + 16x^3 + 5.