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Chapter 1: Problem 21

Find the domain of each function. $$g(x)=\sqrt{5 x+35}$$

Short Answer

Expert verified
The domain of the function \(g(x) = \sqrt{5x + 35}\) is \(x \geq -7\)

Step by step solution

01

Identify the main component of the function

The first step is to recognize that the entire function hangs on the value under the square root sign, which is \(5x + 35\). For the function to have real values, \(5x + 35\) must be either positive or zero.
02

Set an inequality equation

Because we want to find the range of values for 'x' that make the function work, we can set up the inequality \(5x + 35 \geq 0\)
03

Solve the inequality

To solve for 'x', we need to subtract 35 from both sides of the inequality, which gives \(5x \geq -35\). Then, divide both sides by 5 to isolate 'x', resulting in \(x \geq -7\)

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