TITLE: How to get the inverse of this function?
QUESTION [1 upvotes]: I have the function f(x) = (1+8x) / (3-3x).
I have been stuck on trying to get the inverse of this function by isolating for y. I ended up with:
x = (1+8y) / (3-3y) but I am not quite sure where to go from there.

REPLY [0 votes]: Here we start with $$f(x) = \frac{1+8x}{4-3x}$$
So we set $y = f(x)$ and solve for $x$ in terms of $y$:
$$y = \frac{1+8x}{4-3x}$$
$$(4-3x)y = 1+8x$$
$$4y - 3xy = 1+8x$$
$$4y - 3xy - 1 = 8x$$
$$4y - 3xy - 1 - 8x = 0$$
$$-3xy - 1 - 8x = -4y$$
$$-3xy -8x = -4y+1$$
$$-3x(y+8/3) = -4y+1$$
$$-3x = \frac{-4y+1}{y+8/3}$$
$$x = \frac{4y-1}{3y+8}$$
What we have essentially done is find a general equation in terms of $x$ and $y$.  Then, we reverse the process.  Can you see how the general method works?
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