SOLUTION: Given that f(x) = 1/x and (f/g)(x) = (x + 1)/(x^2 - x), find the function g. Let me see. I know that (f/x)(x) means f(x)/g(x). I think the set up is this: (1/

Algebra ->  Functions -> SOLUTION: Given that f(x) = 1/x and (f/g)(x) = (x + 1)/(x^2 - x), find the function g. Let me see. I know that (f/x)(x) means f(x)/g(x). I think the set up is this: (1/      Log On


   

Question 1208025: Given that f(x) = 1/x and (f/g)(x) = (x + 1)/(x^2 - x), find the function g.

Let me see.

I know that (f/x)(x) means f(x)/g(x).

I think the set up is this:

(1/x)/g(x) = (x + 1)/(x^2 - x)

I must find g(x).

You say?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

I'll denote f(x) as simply f. A similar story will apply for g as well.

f/g = (x+1)/(x^2-x)
(1/x)/g = (x+1)/(x^2-x)
1/(x*g) = (x+1)/(x(x-1))
x*1/(x*g) = x*(x+1)/(x(x-1)) ..... multiply both sides by x.
1/g = (x+1)/(x-1)
g(x) = (x-1)/(x+1) is the final answer.

Verification using WolframAlpha
https://www.wolframalpha.com/input?i=f%28x%29%2Fg%28x%29+when+f%28x%29+%3D+1%2Fx+and+g%28x%29+%3D+%28x-1%29%2F%28x%2B1%29

GeoGebra is another option.
I recommend using the CAS tool in GeoGebra.