Question

Find functions f and g so that h(x)=(f∘g)(x). h(x)=5^x −1 (Neither function may be the identity f(x)=x)

Answer 1

To Find functions f and g that satisfy h(x)=(f∘g)(x)=5^x - 1, choose g(x) = 5^x and f(x) = x-1. Composing these functions yields the desired h(x).

Step-by-step explanation:

The question is asking to Find functions f and g such that the composite function (f∘g)(x) equals h(x)=5^x − 1. To find such functions, one can manipulate the given function h(x) into two separate functions that when composed, yield the original function h(x). We can choose for function g(x) to be 5^x and for function f(x) to be x-1. So, g(x) maps x to 5^x, and f(x) then takes that result and subtracts 1 to give us 5^x - 1.