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Chapter 2: Problem 22

Find the domain of each function. $$g(x)=\sqrt{7 x-70}$$

Short Answer

Expert verified
The domain of the function \(g(x) = \sqrt{7 x - 70}\) is \(x \geq 10\).

Step by step solution

01

Set the Radicand Greater Than or Equal to Zero

In this step, the inequality is set up from the radicand of the function. Thus, \(7 x - 70 \geq 0\). The goal here is to find the valid values of \(x\) for which \(g(x)\) is defined.
02

Solve the Inequality

To solve the inequality \(7 x - 70 \geq 0 \), first add 70 to both sides to isolate the term with \(x\), resulting in \(7x \geq 70\). Then divide both sides by 7 to solve for \(x\), which gives the result \(x \geq 10\). These are the values of \(x\) for which the function \(g(x)\) is defined.

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