Question

Given the definitions of f(x) and g(x) below, find the value of (f ∘ g)(0).

f(x) = x^2 - 6x - 7
g(x) = 3x + 7

Answer 1

To find the value of (f ∘ g)(0), substitute g(x) = 3x + 7 into f(x) = x^2 - 6x - 7 to get (f ∘ g)(x) = 9x^2 + 24x. Substitute x = 0 to find (f ∘ g)(0) = 0.

Step-by-step explanation:

To find the value of (f ∘ g)(0), we first need to find the composite function f ∘ g. The composite function f ∘ g is given by (f ∘ g)(x) = f(g(x)).

Substituting g(x) = 3x + 7 into f(x) = x^2 - 6x - 7, we get:

(f ∘ g)(x) = (3x + 7)^2 - 6(3x + 7) - 7 = 9x^2 + 42x + 49 - 18x - 42 - 7 = 9x^2 + 24x

To find (f ∘ g)(0), we substitute x = 0 into the equation:

(f ∘ g)(0) = 9(0)^2 + 24(0) = 0