Suppose the real functions \(f\) and \(g\) both have domain \(\mathbb{R}\). Which condition ensures that the quotient function \(\frac{f}{g}\) also has domain \(\mathbb{R}\)?

Correct answer: \(g(x)\ne 0\ \forall x\in\mathbb{R}\)

Although \(f\) is defined for every real \(x\), \(\frac{f(x)}{g(x)}\) is defined only when \(g(x)\ne0\). Hence C is correct. Being one-one does not prevent \(g\) from taking value zero. In exams, solve \(g(x)=0\) first to find excluded inputs.