If f(x-3) = g(3x-2), find g(x)

Question

So, if $f(x-3) = g(3x-2)$ , find $g(x)$. My question is basically that; how do you get a function from two results of functions, not knowing what the function is.

Answer 1

The question is misleading / poorly stated.

The correct question is this:

If $f(x-3) = g(3x-2)$ holds for every $x$, then what is $g(x)$?

Let $x=3y-2$. Then, $y=\dfrac{x+2}3$.

$g(x) = g(3y-2) = f(y-3) = f\left(\dfrac{x+2}3-3\right) = f\left(\dfrac{x-7}3\right)$.