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C3 Inverse Functions - Mixed Ex. 2F

Been sat for an hour trying to work out how to rearrange this to find the answer and I can't work it out :frown: Can anyone show me how?



The answer is 2x/(x-1)
Screen Shot 2014-07-07 at 00.33.24.png17.5KB
Original post by grn
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xx−2=1+2x−2 \displaystyle \frac {x}{x-2} = 1+\frac {2}{x-2}

Hope this helps. :smile:
Original post by lazy_fish
xx−2=1+2x−2 \displaystyle \frac {x}{x-2} = 1+\frac {2}{x-2}

Hope this helps. :smile:

You don't even need to do this, some simple factorising should give you the answer.

y=xx−2⇒y(x−2)=xy=\dfrac{x}{x-2} \Rightarrow y(x-2)=x

yx−2y=xyx-2y=x

yx−x=2yyx-x=2y

x(y−1)=2yx(y-1)=2y

x=2yy−1⇒f−1(x)=2xx−1x=\dfrac{2y}{y-1} \Rightarrow f^{-1}(x)=\dfrac{2x}{x-1}
(edited 9 years ago)

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