$f(x+1/x)=x^2+1/x^2$, find f(x) In the above question,I get to solve that f(x)=x^2-2 but what i miss in my answer is that absolute value of x is greater than 2 always. I have two questions,first,how do we come to the statement that absolute value of x is greater than 2 here(In the question in my textbook,its given that x belongs to R-{0}. Why do we meed to do the absolhte value thing?)
And second is how to prepare myself whenever I encounter such questions so that I know what I have to look for,for finding range and domain of the expression.
Assuming you're reporting the problem exactly as written, you're puzzled about finding the "solution" to an appallingly badly stated problem.
For instance, if I tell you I have a function $f$, and that I know that for any real $x$, it's true that $$ f(x^2) = x^2 $$ you cannot conclude anything about the domain of $f$ except that it must include all nonnegative real numbers.
For instance, I might have been thinking about the function from the reals to the reals defined by $x \mapsto x$; that function has the property stated.
I might also have been thinking about $f(x) = |x|$, or thinking about $$ f(x) = \begin{cases} x & x \ge 0 \\ -13 & x < 0\end{cases}, $$ or about $$ f : \Bbb R^{+} \cup \{0\} \to \Bbb R^{+} \cup \{0\}: x \mapsto x. $$
All these functions have the property that I specified, but they have varying domains, and varying images and even have varying codomains.
So I guess my recommendation would be "Try not to sweat too much about solving problems like these; instead, watch carefully for them and run away from anyone who asks you to 'solve' such things."