Problem 22 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.