Problem

Consider the function \(f(x) = \sqrt{x} \) and \(g(x) = x^2 \). Find the domain and range of \((f+g)(x)\), \((f-g)(x)\), \((fg)(x)\), and \((f/g)(x)\).

Answer

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Answer

For \(f/g\), the domain is all \(x\) such that \(x\geq 0\) and \(x\neq 0\). The range is \(y\geq 0\).

Steps

Step 1 ：For \(f+g\), the domain is all \(x\) such that \(x\geq 0\) and \(x\in\mathbb{R}\). The range is \(y\geq 0\).

Step 2 ：For \(f-g\), the domain is all \(x\) such that \(x\geq 0\) and \(x\in\mathbb{R}\). The range is \(y\leq 0\).

Step 3 ：For \(fg\), the domain is all \(x\) such that \(x\geq 0\) and \(x\in\mathbb{R}\). The range is \(y\geq 0\).

Step 4 ：For \(f/g\), the domain is all \(x\) such that \(x\geq 0\) and \(x\neq 0\). The range is \(y\geq 0\).

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