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':
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| 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)..