Find the Domain of \(f(x)=\frac1{x-7}\)
Question:
Find the domain of the following real valued function of real variable:
$$
f(x)=\frac1{x-7}
$$
Solution
Given: $$ f(x)=\frac1{x-7} $$
The denominator cannot be zero.
Therefore, $$ x-7\ne0 $$
$$ x\ne7 $$
Hence, all real numbers except \(7\) are allowed.
Therefore, the domain is: $$ \mathbb{R}-\{7\} $$
or $$ (-\infty,7)\cup(7,\infty) $$