Identify the inverse of f(x) = x^2 − 4. Determine whether it is a function and state its domain and range. I know that it's not a function because of the horizontal-line test, but I don't know how to find the domain and range!

Question

meehan98 · Answer

@pooja195

thomas5267 · Answer

Let $f^{-1}(x)$ denote the inverse of $f(x)$.
The domain of $f(x)$ is the range of $f^{-1}(x)$.
The range of $f(x)$ is the domain of $f^{-1}(x)$.
The domain of a function is the set of numbers such that the output of that function (i.e. range) is real numbers (at least for now, things get more complex as you learn).
The range of a function is the set of outputs of the function.
For example, the $f(x)$ has domain of $\mathbb{R}$ (real numbers) since for every real number you put into the function you will get a real number out.
The range of $f(x)$ is $[-4,\infty )$ since the smallest output $f(x)$ can get is -4 (corresponding to x=0) and there is no upper limit on how big $f(x)$ can get.

misty1212 · Answer

HI!!

meehan98 · Answer

Okay, thanks for your help! I will have to do a little bit more research because this seems very difficult.