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For $f(x) = 1/(2-x)$.

Apologies for this overtly simplistic question; am I missing something deeper/more meaningful in this homework question or is it as simple as $m=1$?

In terms of context, the previous questions asked to determine the domain of function and it's compositions with other functions. I'm not sure how this question (as part of the same set) has to do with domains if any.

If I'm overlooking something, I would greatly appreciate a nudge/hint in the right direction as to what should consider before applying Occam's razor.

Thank you!

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    for m=1, any value of x satisfies the equation, for m=0, only x=0 satisfies it.2012-03-18

2 Answers 2

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The question can be rephrased as follows: for which $m$ does the equation $\frac1{2-mx}=\frac1{2-x}$ have a solution? If you try to solve this equation, you find that you must have $2-x=2-mx\;,$ and hence $x=mx$. This certainly has a solution when $m=1$, but in fact it has a solution for lots of other values of $m$ as well. What are they? (Note: for these values it has only one particular solution.)

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    @BrianM.Scott I just cooked an answer compiling all the ingredients from the comments.2012-03-18
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$(m,x)$ can have the following values,

when $m=1$ , $x$ can be any real number (except 2)

when $x=0$ , $m$ can be any real number,

when $m=-1$, $x$ has to be $0$.

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    Yes very true, I just edited the answer, thanks for pointing that out @xlm2012-03-18