Find the domain of the difference of the functions \(f(x) = \sqrt{x}\) and \(g(x) = \frac{1}{x}\).
Answer
Step 3: The domain of the difference of the functions \(f(x) - g(x)\) is the set of all x-values that are in both the domain of \(f\) and the domain of \(g\). This means that we need to find the intersection of the two domains. The intersection of \(x \geq 0\) and \(x \neq 0\) is \(x > 0\).
Step 1 ：Step 1: We need to find the domain of each individual function first. The domain of \(f(x) = \sqrt{x}\) is \(x \geq 0\), because we cannot take the square root of a negative number.
Step 2 ：Step 2: The domain of \(g(x) = \frac{1}{x}\) is \(x \neq 0\), because we cannot divide by zero.
Step 3 ：Step 3: The domain of the difference of the functions \(f(x) - g(x)\) is the set of all x-values that are in both the domain of \(f\) and the domain of \(g\). This means that we need to find the intersection of the two domains. The intersection of \(x \geq 0\) and \(x \neq 0\) is \(x > 0\).
