Question

Please people

Find the function h(x) = f(x) ∘ g(x) if f(x) = x(2 - x) and g(x) = 3^x.


A. h(x) = 0

B. h(x) = -3^2x

C. h(x) = 2(3^2x)

D. h(x) = 3^x (2 - 3^x)

Answer 1

D

Explanation:

Function composition substitutes more than just values or constants. It substitutes functions inside another function. Solve each expression by starting inner most and working to outermost. The expression f(x) ∘ g(x) means f(g(x)).

Let f(x) = x(2 - x) and g(x) = 3^x.

Begin by substituting g(x) in for x in f(x).

`f(g(x)) = (3^x)(2-(3^x))`

The solution is D.