Question

Let f be a function from R to R defined by f(x) = x^2. Find f^–1({x | 0 < x < 1}).

So I found the inverse of f(x):
f^-1(x) = sqrt(x)
But now how do I continue to ensure that it is only for 0 < x < 1?

Answer 1

it is actually good for all x >= 0
The other branch is -√x

You can check the inverse by making sure that (√x)^2 = √(x^2) = x
This is true for all x >= 0

for x < 0, √(x^2) = -x and √x is not real

Answer 2

Thank you for your response. But I would like to know what you would put as a final answer to the problem. Because it seems that the solution I found ( f^-1(x) = √x ) is valid for 0 and ALL positive real numbers because the domain and co-domain are the real numbers. But not all positive real numbers are less than 1, and 0 certainly isn't. So what exactly does "find f^–1({x | 0 < x < 1})" mean?