Given f(x) = 1/x and (f/g)(x) = (x + 1)/(x^2 - x), find the function g. I know that (f/g)(x) is f(x)/g(x). I also know that f(x) = 1/x. I have (1/x)/g(x) = (x + 1)/(x^2 - x). Is this correct thus far? If so, what's the next step?
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Originally Posted by harpazo Given f(x) = 1/x and (f/g)(x) = (x + 1)/(x^2 - x), find the function g. I know that (f/g)(x) is f(x)/g(x). I also know that f(x) = 1/x. I have (1/x)/g(x) = (x + 1)/(x^2 - x). Is this correct thus far? If so, what's the next step? So far, so good. I'd cross multiply. That is, use the fact that if $\displaystyle \frac{a}{b}=\frac{c}{d}$ then $\displaystyle ad = bc$. Then get g(x) on its own.
Let (1/x)/g(x) = (x + 1)/(x^2 - x) I can make g(x) the subject: g(x) = (1/x)/[(x + 1)/(x^2 - x)] g(x) = (x^2 - x) / [(x + 1) * x] g(x) = x(x - 1) / [(x + 1) * x] g(x) = (x - 1)/(x + 1) Yes?
Correct!
Originally Posted by Debsta Correct! Another one in the books.