Given the functions \(f(x) = \sqrt{x}\) and \(g(x) = \frac{1}{x}\), find the domain of the product of the functions \(h(x) = f(x)g(x)\).
Answer
Step 3: Therefore, the domain of \(h(x) = f(x)g(x)\) is \(x > 0\).
Step 1 ：Step 1: Determine the domain of each function separately. The domain of \(f(x)\) is \(x \geq 0\) because the square root of a negative number is undefined. The domain of \(g(x)\) is \(x \neq 0\) because division by zero is undefined.
Step 2 ：Step 2: The domain of the product of the functions is the intersection of their individual domains. So, \(h(x)\) is defined for \(x \geq 0\) and \(x \neq 0\). But, 0 is not included in the domain of \(g(x)\), so it should also be excluded from the domain of \(h(x)\).
Step 3 ：Step 3: Therefore, the domain of \(h(x) = f(x)g(x)\) is \(x > 0\).
