Determining the domain and range for the function ##f^{-1}##

[angela107]

Homework Statement

For this question, let $f:[0,+∞)->R$ is defined by $f(x) = √x$, and let $f^{-1}(x)$ be its inverse function. What is the domain and range of the function $f^{-1}(x)$?

Relevant Equations

n/a

The domain and range of this function will be the same.

We can let $𝑓(𝑥)=\sqrt{x},𝑥≥0$

However, $𝑦=𝑓(𝑥)≥0$, so the domain and range of $f$ are $[0,+∞)$

And since $f$ is a function, $f^{-1}s$ domain is the range of $f$ and $f^{-1}s$ range is $f’s$ domain.

In other words, the domain and range of $f^{-1}:[0,+∞)→[0,+∞)$.

Is my solution correct?

 

[anuttarasammyak]

Hi. It seems all right.

 

[Mark44]

The work is correct. The domain and range for this function are the same -- $[0, \infty)$, so the domain and range for its inverse are also the same sets.