# Thread: Find the function g

1. ## Find the function g

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?

2. ## Re: Find the function g

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.

3. ## Re: Find the function g

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!

5. ## Re: Find the function g

Originally Posted by Debsta
Correct!
Another one in the books.