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Let $f(x)=\dfrac{x}{x-7}$. Find a function $y=g(x)$ so that $(f\circ g)(x)=x$.

Does anyone have any ideas on how to do this? I've exhausted all sorts of possibilities and I am now clueless. (On a side note, this is not homework, but rather an optional online assignment I was given. It's really puzzling me.)

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    Replace the $x$ with $y$ and the $f(x)$ with $x$, and solve for $y$.2011-09-10

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So you want $$\frac{g(x)}{g(x)-7}= x \Longrightarrow g(x)= x\cdot g(x) - 7x $$

Solve for $g(x)$ from here.

If you still can't complete, then take a look below.

$$ x \cdot g(x)- g(x) = 7x \Longrightarrow g(x) \cdot \bigl(x-1\bigr) = 7x$$

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    So is the solution 7x / x-1?2011-09-10
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    @Mike: Yes, it is.2011-09-10
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    @Mike: Mind your parentheses. :) Better to write it as 7x/(x-1) to avoid ambiguity.2011-09-10