Question

I've had a major brain fart..How do you get the inverse function of:
f(x)= (2x-3)/(x+1)
i know the answer but i don't know how to get there.
Please help, thanks.

Answer 1

original
y = (2x-3)/(x+1)

first step is to interchange the x and y variables

so the inverse equation is
x = (2y-3)/(y+1)
but we probably want to write this as a function, so we have to solve for y
-- cross-multiply

xy+x = 2y - 3
xy - 2y = -3 - x
y(x-2) = -3-x
y = (-3-x)/(x-2)
or
y = (x+3)/(2-x)

I usually test it by letting any x in the first to get the y.
Then by plugging this y answer as an x-value into the new function I should get the original number back
e.g.
let x = -2
then y = (-4-3)/(-2+1) = 7

into the new one:
let x = 7
y = (7+3)/(2-7) = 10/-5 = -2

all is good