Problem

Give the domain of the function defined below. \[ f(x)=(x-10)^{1 / 2} \] The domain is $\square$. (Simplify your answer. Type your answer in interval notation.)

Solution

Step 1 :Given the function \(f(x)=(x-10)^{1 / 2}\).

Step 2 :The function is defined for all \(x\) such that \((x-10)^{1 / 2}\) is a real number.

Step 3 :This is true for all \(x\) such that \(x-10 \geq 0\).

Step 4 :Solving the inequality, we find that \(x \geq 10\).

Step 5 :Therefore, the domain of the function is \([10, \infty)\).

Step 6 :\(\boxed{[10, \infty)}\) is the final answer.

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Source: https://solvelyapp.com/problems/ZSreRyQxqE/

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