Question

Express the function h(x)=1x−5 in the form f∘g. If
g(x)=(x−5), find the function f(x).

Answer 1

To express the function h(x)=1x−5 in the form f∘g, we substitute the given function g(x) into h(x) and simplify. The function f(x) that satisfies h(x) = f(g(x)) is f(x) = x−10.

Step-by-step explanation:

To express the function h(x)=1x−5 in the form f∘g, we need to find two functions, f(x) and g(x), such that h(x) = f(g(x)). Given that g(x) = (x−5), we can substitute this into h(x) to get h(x) = 1(x−5)−5. Now, we have h(x) = x−10. Therefore, f(x) = x−10 is the function that satisfies h(x) = f(g(x)).

Answer 2

To express the function h(x) = 1x - 5 in the form f∘g, we need to find the function g(x) and the function f(x). Given that g(x) = (x - 5), the function f(x) = x - 10.

Step-by-step explanation:

To express the function h(x) = 1x - 5 in the form f∘g, we need to find the function g(x) and the function f(x).

Given that g(x) = (x - 5), we can substitute this expression into h(x) to get:

h(x) = 1(g(x)) - 5 = 1(x - 5) - 5 = x - 10.

Therefore, the function f(x) = x - 10.