Let f(x) = (x+3) / (x−1) . Find f^-1 (x).

Answer 1

In finding inverses, we find x as a function of y, then substitute x for y.

y = (x+3)/(x-1)

xy - y = x + 3

xy - x = y + 3

x(y - 1) = y + 3

x = (y+3)/(y-1)

Substituting x for y, we get

f^-1(x) = (x+3)/(x-1)

Note that f^-1(x) = f(x)

Answer 2

Begin by replacing f(x) with y in the original equation:

y = (x+3)/(x-1)

Then, we want to solve for x in terms of y — that is, isolate the x on one side of the equation, leaving the y's on the other side. The main steps of this process are as follows:

y*(x-1) = x+3

yx - y = x + 3

xy - x = y + 3

x(y-1) = y+3

x = (y+3)/(y-1)

The last step is to invert the x and y (so, x becomes y and y becomes x):

y = (x+3)/(x-1)

This is the inverse function (which in this example is identical to the original function)

Answer 3

x = (y + 3) / (y - 1)

x = 1 + [3 / (y - 1)]

Answer 4

Answer 5

to invert that equation you solve for x in this equation:

y = (x + 3)/(x - 1)

multiply both sides by x-1 and distribute the y on the left side

xy - y = x + 3

collect x terms on the left side

x(y-1) - y = 3

solve for x

x = (y + 3)/(y - 1)

f^-1(x) = (y + 3)/(y - 1)