If r is a linear function with the slope that is not equal to zero which of the following is always true of its inverse function

Let's make up a linear function:  y = mx + b.

Find its inverse:

1) interchange x and y:   x = my + b                      x-b
2) solve this result for y:        my = x - b, or   y =
                                                                                m
                             -1
3) replace y by  f      (x)

So long as m is not zero, this function is defined for all x.