#1**+2 **

f(x) = (x - 3)/(x - 4)

First let's find f^{-1}(x) . Instead of f(x) , write y .

y = (x - 3)/(x - 4)

Now solve for x . Multiply both sides of the equation by (x - 4) .

y(x - 4) = x - 3

xy - 4y = x - 3

Add 4y to both sides and subtract x from both sides.

xy - x = 4y - 3

Factor x out of the terms on the left side.

x(y - 1) = 4y - 3

Divide both sides by (y - 1) .

x = (4y - 3)/(y - 1)

So...

f^{-1}(x) = (4x - 3)/(x - 1)

And...

(4x - 3)/(x - 1) is undefined when x - 1 = 0

f^{-1}(x) is undefined when x = 1

hectictar Jan 25, 2018