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Inverse functions

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.
 Graph of y = 4x + 3 and its inverse
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':

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

1 comment:

1. The point of inverse functions is to cancel or collapse
a 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)..