Notation
The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. The inverse of a function does not mean the reciprocal of a function.
Inverses
A function normally tells you what y is if you know what x is. The inverse of a function will tell you what x had to be to get that value of y.
A function f -1 is the inverse of f if
<span><span>for every x in the domain of f, f<span> -1</span>[f(x)] = x, and</span><span>for every x in the domain of f<span> -1</span>, f[f<span> -1</span>(x)] = x</span></span>
The domain of f is the range of f -1 and the range of f is the domain of f<span> -1</span>.
Graph of the Inverse Function
The inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched. That is, if (4,6) is a point on the graph of the function, then (6,4) is a point on the graph of the inverse function.
Points on the identity function (y=x) will remain on the identity function when switched. All other points will have their coordinates switched and move locations.
The graph of a function and its inverse are mirror images of each other. They are reflected about the identity function y=x.
