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Chapter 2: Problem 111

Find the domain of \(h(x)=\sqrt{36-2 x}\).

Short Answer

Expert verified
The domain of \(h(x)= \sqrt{36-2x}\) is \(x \leq 18\). For all \(x\) in this interval, \(h(x)\) is defined in the real number system.

Step by step solution

01

Identify the radicand

Here, the function is \(h(x)= \sqrt{36-2x}\). The radicand, i.e., the term under the square root, is \(36-2x\). The task now is to find the values of \(x\) that will make this term non-negative.
02

Set up an inequality equation

We want to find when the radicand, \(36-2x\), is non-negative, so we set up the inequality \(36-2x \geq 0\).
03

Solve the inequality

We can solve the inequality for \(x\) by first subtracting 36 from both sides to obtain \(-2x \geq -36\), and then dividing both sides by -2. Remember, dividing or multiplying both sides of an inequality by a negative number reverses the direction of the inequality. Hence we get \(x \leq 18\).

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