Question

Given the function h(x) below, decompose h(x) into component functions f(x) and g(x) so that h(x)=f(g(x)).

h(x)=2/(−9x+8)9

Answer 1

The function h(x) = 2/(-9x + 8)^9 can be decomposed into g(x) = -9x + 8 for the inner function, and f(x) = 2/x^9 for the outer function, resulting in the composite function h(x) = f(g(x)).

Step-by-step explanation:

The function h(x) = 2/(-9x + 8)^9 can be decomposed into two component functions f(x) and g(x) such that h(x) = f(g(x)). One possible decomposition is:

• Let g(x) = -9x + 8. This function represents the inner operation inside the parenthesis.
• Then let f(x) = 2/x^9. This function represents the outer operation where the result of g(x) is taken to the power of 9 and then multiplied by 2.

Therefore, h(x) = f(g(x)) = 2/((-9x + 8)^9), which is the original function expressed as the composition of the two functions f and g.