verify that f and g are inverse functions.

f(x) = 5x^2
x>(or equal too)0
g(x)= (x+2/5)^1/2

Find the inverse of f and see if it is g.

To verify whether f and g are inverse functions, we need to show that applying f followed by g (or g followed by f) yields the original input.

Let's start by composing f and g:

f(g(x)) = f((x+2/5)^(1/2))
= 5((x+2/5)^(1/2))^2
= 5(x+2/5)
= 5x + 2

Now, let's compose g and f:

g(f(x)) = g(5x^2)
= (5x^2 + 2/5)^(1/2)

If f and g are inverse functions, then f(g(x)) = x, and g(f(x)) = x should hold true for all x in the domain of f.

Let's check:

f(g(x)) = 5x + 2
g(f(x)) = (5x^2 + 2/5)^(1/2)

Since f(g(x)) does not equal x, and g(f(x)) does not equal x for all x in the domain of f, we can conclude that f and g are not inverse functions.