The inverse of a function is its reflection in the line y = x. The following graph shows the function `f(x) = 4x + 3` and its inverse `f^-1(x) = (x - 3)/4` and the line of reflection `y = x`.

In order to find the inverse of a function, solve its equation for the independent variable, which is generally 'x'. For example for the function `y = 4x + 3`, in order to find its inverse, solve the equation for 'x':

Graph of y = 4x + 3 and its inverse |

`y = 4x + 3`

`y - 3 = 4x`

`(y - 3)/4 = x`

Exchanging x and y,

`y = (x - 3)/4``y = (x - 3)/4` is the inverse of `y = 4x + 3`

The point of inverse functions is to cancel or collapse

ReplyDeletea function back to the unchanged diagonal line x=y.

One test is to plug the inverse into the function to see

if the result is 'x', the starting point before modification by f(x)..