If \(f(x)=\frac{x^2-4}{x-2}\), where \(x\ne 2\), what is the range of \(f\)?

Correct answer: \(\mathbb{R}\setminus\{4\}\)

Since \(x^2-4=(x-2)(x+2)\), for \(x\ne2\) we have \(f(x)=x+2\). The value \(4\) would occur only when \(x=2\), but that input is excluded from the domain. Conversely, for every \(y\ne4\), choosing \(x=y-2\ne2\) gives \(f(x)=y\). Hence the range is \(\mathbb{R}\setminus\{4\}\). Exam tip: after simplifying a rational function, check whether an excluded input removes a corresponding output value.