SOLUTION: show that (g of f)(x)=x and (f of g)(x)=x f(x)=2/(1-x) g(x)=(x-2)/x

Algebra ->  Functions -> SOLUTION: show that (g of f)(x)=x and (f of g)(x)=x f(x)=2/(1-x) g(x)=(x-2)/x      Log On


   

Question 681877: show that (g of f)(x)=x and (f of g)(x)=x
f(x)=2/(1-x)
g(x)=(x-2)/x
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
(gof)(x) = %28%282%2F%281-x%29%29-2%29%2F%282%2F%281-x%29%29
= %28%282%2F%281-x%29%29-2%29%28%281-x%29%2F2%29
...
= %28%282%2F%281-x%29%29-2%28%281-x%29%2F%281-x%29%29%29%28%281-x%29%2F2%29
...
= %28%282-2%281-x%29%29%2F%281-x%29%29%28%281-x%29%2F2%29
...
= %28%282-2%2B2x%29%2F%281-x%29%29%28%281-x%29%2F2%29
...
= %28cross%282%29x%2Fcross%28%281-x%29%29%29%28cross%28%281-x%29%29%2Fcross%282%29%29
...
= x
(fog)(x) = 2%2F%281-%28%28x-2%29%2Fx%29%29
= 2%2F%281%28x%2Fx%29+-+%28%28x-2%29%2Fx%29%29
...
= 2%2F%28%28x-%28x-2%29%29%2Fx%29%29
...
= 2%2F%28%28x-x%2B2%29%2Fx%29
...
= cross%282%29%28x%2Fcross%282%29%29
...
= x
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