What is the range of the function \(f(x)=\frac{1}{x}\), where \(x\neq 0\)?

Correct answer: \(\mathbb{R}\setminus\{0\}\)

The function \(f(x)=\frac{1}{x}\) can never have the value \(0\), since \(\frac{1}{x}=0\) has no real solution for \(x\neq 0\). Also, for every nonzero real number \(y\), taking \(x=\frac{1}{y}\) gives \(f(x)=y\). Hence, the range is \(\mathbb{R}\setminus\{0\}\). Option \(\mathbb{R}\) is incorrect because it includes \(0\). Exam tip: For the reciprocal function \(\frac{1}{x}\), both domain and range exclude \(0\).