hey all, need help with a problem
Question: Use composition to show that f(x) = (x + 3) / (x - 2) and g(x) = (2x - 3) / (x - 1) are inverse of each other.
Any help would be greatly appreciated, thanks
-Laconian
You are being asked to verify that f(g(x)) = x and that g(f(x)) = x. For the first of those, you need to see whether $\displaystyle \frac{\frac{2x-3}{x-1} +3} {\frac{2x-3}{x-1} - 2} = x$. But before you spend any time trying to simplify that compound fraction, I suggest that you look at the question again, because as it stands, there's a mistake. Those two functions are not inverses of each other. (In fact the 3s in the two numerators ought to have the same sign, either both + or both -.)