Question

Is f(x) the inverse function of g(x)?

3
f(x) = √√x + 5
g(x) = 320x
yes
3
no

Answer 1

The function f(x) = √√x + 5 is not the inverse of g(x) = 3^20x. To be inverses, the composition of f(g(x)) and g(f(x)) should result in the identity function, returning x. In this case, they do not satisfy this condition.

Step-by-step explanation:

The question asks if the function f(x) is the inverse of the function g(x), where f(x) = √√x + 5 and g(x) = 3^20x. The properties of inverse functions state that applying one function followed by its inverse will yield the original value. Hence, if f(g(x)) = x and g(f(x)) = x, then f(x) and g(x) are inverses.

To check if these two functions are inverses, we could substitute g(x) into f(x) and vice versa and simplify to see if we get x.

However, based on the equation f(x) = √√x + 5, it is apparent that no real inverse of the form given for g(x) will satisfy the inverse properties when composed with f(x).

Therefore, f(x) is not the inverse of g(x).