Question

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

[h(x) = frac1/x - 5]

a) (f(x) = frac1/x), (g(x) = x - 5)
b) (f(x) = frac1/x - 5), (g(x) = x)
c) (f(x) = x), (g(x) = frac1/x - 5)
d) (f(x) = x - 5), (g(x) = frac1/x)

Answer 1

To decompose the given function h(x) = frac1/x - 5 into component functions f(x) and g(x) so that h(x) = f(g(x)), we need to find two functions whose composition will yield the given function. The correct answer is (f(x) = x - 5), (g(x) = frac1/x), which is option d.

Step-by-step explanation:

To decompose the given function h(x) = frac1/x - 5 into component functions f(x) and g(x) such that h(x) = f(g(x)), we need to find two functions whose composition will yield the given function.

We can rewrite the function as h(x) = frac{1}{x} - 5. From this, we can identify that g(x) = frac{1}{x} and f(x) = x - 5. When we substitute g(x) into f(x), we get f(g(x)) = (frac{1}{x}) - 5 which is equal to h(x). Therefore, the correct answer choice is (f(x) = x - 5), (g(x) = frac{1}{x}) which is option d.