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Question 942570: I'm unsure as to the answer given by BBC bitesize to one of their problems, the problem itself being f(x) = (x-1)/(x+1) find ff(x).
So I've gotten as far as (-2/(x+1)) * ((x+1)/(2x)) which equates to (according to me) -2x-2/2x^2+2x, now BBC show the answer to be 1/x which I do not get, however I think the answer is 1/x^2 (assuming that -x and x cancel eache other, which I'm also not entirely sure is allowed), so yeah that's my problem...
(Link to problem: http://www.bbc.co.uk/bitesize/higher/maths/algebra/functions/revision/3/)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! f(x) = (x-1)/(x+1) find fof(x).
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f[f(x)] = f[(x-1)/(x+1)]
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= [(x-1)/(x+1)-1] / [(x-1)/(x+1)+1]
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= [[x-1-(x+1)]/(x+1)] / [[x-1 + (x+1)]/(x+1)]
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= [-2/(x+1)] / [2x/(x+1)]
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= -2/2x
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= -1/x
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Cheers,
Stan H.
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