# Thread: Inverse function of a closed set???

1. ## Inverse function of a closed set???

This is a textbook problem...
f:R->R
f(x) = x^2
(i)Find f^-1(25).
(ii)Find f^-1([4, 25])
The first one is easy but how do I do the 2nd one? I've never encountered something like this.
I suppose
Let f^-1([4,25])=x
or, f(x)=[4,25]
or, x^2=[4,25]
...and then?

2. (ii)Find $f^-1([4, 25])
$

This is just asking you to find all x in the domain taht get mapped into the interval [4,25]

So $x^2\in[4,25]$

So $2\leq x \leq 5$ and also $-5\leq x\leq -2$ (all you do is take the positive and negative square root of the closed set interval)

3. I was thinking something like that. Thanks. Seinfeld rules BTW(assuming that's where you got your name)