Inverse+functions

=Inverse functions= Sept 19/11

The 'inverse' of some function **f** is denoted by **f^-1**. Remember that this does not refer to the function x^-1! Graphically, the inverse of a function can be created by reflecting the function over the y=x line: Linear function and it's inverse Quadratic function and it's inverse In terms of a mapping diagram: Table of values:
 * x || f(x) ||
 * 1 || 4 ||
 * 2 || 3 ||
 * 3 || 2 ||
 * 4 || 1 ||

Algebraically (probably the most useful and important) When finding the inverse of a function using algebra, simply #1 switch the output (ie. y) and the input (ie. x) and Example: f(x) = x^2 1. y= x^2 2. x= y^2 x= +- sqrt(y) 3. f^-1(x) = +- sqrt(x)
 * x || f^-1(x) ||
 * 4 || 1 ||
 * 2 || 3 ||
 * 3 || 2 ||
 * 4 || 1 ||
 * 1) 2 solve for the output.

As you can see from the examples above, sometimes the inverse of a function is a function, sometimes no. (ie. f(x)=x^2) A good way to test whether your inverse function is correct is to take the output of f(x) and input it into f^-1(x), and if your new output is the originally input of f(x) you are correct.

Answers to the introduction quiz coming soon.