+9466 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
