Question

Find functions f(x) and g(x) so the given function can be expressed as

ℎh(x)=f(g(x)).
h(x)=4(x+2)²

a) f(x)=4x, g(x)=(x+2)²
b) f(x)=x+2, g(x)=4x²
c) f(x)=2x, g(x)=(x+2)²
d) f(x)=x², g(x)=4(x+2)

Answer 1

The correct functions f(x) and g(x) for the given expression h(x) = 4(x+2)² are f(x) = 4x and g(x) = (x+2)².

Step-by-step explanation:

To find functions f(x) and g(x) such that h(x) = f(g(x)) where h(x) = 4(x+2)², we need to match the given expression with f(g(x)). Let's compare the given expression with our options:

Option a) f(x) = 4x, g(x) = (x+2)²-

Since f(x) should eliminate the square term, f(x) = 4x is a good choice. Now let's check if g(x) = (x+2)² is valid: g(x) = (x+2)² = x² + 4x + 4 which matches the expression in h(x).

Therefore, the correct answer is a) f(x) = 4x, g(x) = (x+2)².