Given that \( f(x)=6 x^{2}-2 x \) and \( g(x)=2 x \), what is the domain of \( \left(\frac{f}{g}\right)(x) ? \) (1 point) the set of all real numbers except \( x=\frac{1}{3} \) the set of all real numbers the set of all real numbers except \( x=0 \) and \( x=\frac{1}{3} \) the set of all real numbers except \( x=0 \)

To determine the domain of \(\left(\frac{f}{g}\right)(x)\), we need to consider the function \(g(x)\) because the division by zero is undefined. Given \(g(x) = 2x\), it equals zero when \(x = 0\). Therefore, we must exclude \(x = 0\) from the domain. For \(f(x)\), since \(6x^{2} - 2x\) is a polynomial, it is defined for all real numbers. This means that the only restriction comes from \(g(x)\). Thus, the domain of \(\left(\frac{f}{g}\right)(x)\) is the set of all real numbers except \(x = 0\). The correct answer is the set of all real numbers except \(x = 0\).