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**A function f is defined on the set of real numbers by**

f(x)= [tex]\frac{1-x}{x}[/tex] , (x [tex]\neq[/tex] 0)

Find, in its simplest form, an expression for f(f(x))

f(x)= [tex]\frac{1-x}{x}[/tex] , (x [tex]\neq[/tex] 0)

Find, in its simplest form, an expression for f(f(x))

My Attempt:

f(f(x)) = f ( [tex]\frac{1-x}{x}[/tex] ) = ( 1-( [tex]\frac{1-x}{x}[/tex] )) / ( [tex]\frac{1-x}{x}[/tex] )

. . .as you can see, i am rubbish. I know that i am failing to see something. Maybe the following, which will give a further insight to my understanding (or mis), will help someone cure me.

[tex]\frac{1-x}{1}[/tex] = [tex]\frac{1}{x}[/tex](1-x) = [tex]\frac{1}{x}[/tex] -1

That is not correct, is it? Where am i going off the track in my understanding?

One last thing, the text book i am studying has, allegedly, various errors in it, the answer it gives is [tex]\frac{2x-1}{1-x}[/tex] . I can only assume it is right, for now. I just do not see how that answer is arrived at, given the problem.