Question

Given f(x)=1/X and (f/g)(x)=(x+1)/(x^2-x), find the function of g.

Answer 1

Since f is 1/x and f/g is (x+1)/x(x-1) (by pulling out a GCF in the denominator), you're left simply needing to figure out what you divided by to transform 1/x into (x+1)/x(x-1). If I pull out 1/x from the second expression (so that it reads 1/x*(x+1)/(x-1)) you an see that 1/g has to be (x+1)/(x-1),, meaning that g(x)=(x-1)/(x+1). That is, f/g = f*1/g, and after separating out the pieces, you can get g by taking the reciprocal of 1/g. So final answer: g(x)=(x+1)/(x-1).