Definition
For a function:
f(x) = x
A function only has an inverse if only every value x corresponds to some unique value f(x). Another way to state it is the following: A function has an inverse if (and only if) its graph intersects any horizontal line at most once. For example, the function f(x2) does not have an inverse because there are many instances where a horizontal line can intersect the function at more than one location.
Notation
For a function f, it's inverse would be written as f−1
To Find An Inverse
To find an inverse, solve the equation for the opposite variable. For a example, if:
y = x3
its inverse is:
x = y1/3
If:
y = -x + 4
its inverse is:
x = -y + 4
If:
y = -2x − 1
its inverse is:
x = −y/2 − 1/2