Is the inverse of f(x) a function?

Question

if not, how could the domain of f be restricted to make its inverse a function?

Answer 1

The inverse of f(x) is a function if the function f(x) is uniformly increasing or decreasing.  Otherwise the inverse will have two (or more) solutions for a given value.

Answer 2

I need to know what f(x) is, honey *S*

Answer 3

For a function to have an inverse the function must be one-to-one (i.e. if f(a) = f(b) this implies that a = b).   Therefore, you must restrict the domain to an interval such that f(x) is one-to-one on that interval.

Example:  f(x) = x² is not one-to-one on all of its domain because f(1) = f(-1), but 1 ≠ -1.  Therefore, you must find an interval such that f(x) is one-to-one.  Thinking for a bit you'll see that you can restrict its domain to (-∞, 0] or [0, ∞), though you could have chosen something like [1, 298] but that is unnecessary.

Hope this helps!

p.s.  You can read more about it here:

http://en.wikipedia.org/wiki/Inverse_fun...

EDIT:  rscanner is correct, however I probably would recommend you going by that definition because its not the formal definition for the existence of an inverse.  Also in a way, the definition I gave is much more basic as you don't need to know calculus to understand it.