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.