Finding domain of $f \circ g$ I am having a small question, please don't close this before answering, I just want to know whether its a matter of convention or not.
If $f(x) = \dfrac{1}{x}$ and $g(x) = \dfrac{1}{x}$
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Then $f \circ g = x$
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I think domain of $f \circ g $ is $\mathbb{R} - \left\{0\right\}$
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But many ppl I know are having an opinion that domain is $\mathbb{R}$ 
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Which is true, OR is it just a matter of convention.

One sensible way to resolve this issue is to understand what the equation $f \circ g(x)=x$ does and does not say. It does not say "the function $f \circ g(x)$ is the same as the function $x$". By being careful about domains, what this equation does say is that "the function $f \circ g(x)$ is the same as the restriction of the function $x$ to the domain of $f \circ g(x)$", and that domain is the set $\mathbb{R}-\{0\}$, as stated in other answers.
