Questions: Answer the following True or False: Let f and g be functions. Then the domain of f/g is the intersection of the domain of f and the domain of g True False

Solution Steps

To determine if the statement is true or false, we need to consider the definition of the domain of the function \(\frac{f}{g}\). The domain of \(\frac{f}{g}\) is the set of all \(x\) values that are in the domain of both \(f\) and \(g\), except where \(g(x) = 0\). Therefore, the domain of \(\frac{f}{g}\) is the intersection of the domain of \(f\) and the domain of \(g\), excluding the points where \(g(x) = 0\).

To determine the domain of the function \(\frac{f}{g}\), we need to consider the domains of both \(f\) and \(g\). The domain of \(\frac{f}{g}\) includes all \(x\) values that are in the domain of both \(f\) and \(g\), except where \(g(x) = 0\).

The domain of \(\frac{f}{g}\) is the intersection of the domain of \(f\) and the domain of \(g\). However, we must exclude any \(x\) values where \(g(x) = 0\).

Given the above analysis, the domain of \(\frac{f}{g}\) is not simply the intersection of the domain of \(f\) and the domain of \(g\); it also excludes points where \(g(x) = 0\). Therefore, the statement is false.

Final Answer