Find the Domain of \(f(x)=\frac1x\)

Solution

Given: $$ f(x)=\frac1x $$

The denominator of a fraction cannot be zero.

Therefore, $$ x\ne0 $$

Hence, all real numbers except \(0\) are allowed.

Therefore, the domain is: $$ \mathbb{R}-\{0\} $$

or $$ (-\infty,0)\cup(0,\infty) $$