Question

consider the function $f(x) = \sqrt{5x - 5} + 1$. which inequality is used to find the domain? \\(\circ\\ 5x - 4 \geq 0\\) \\(\circ\\ \sqrt{5x - 5} + 1 \geq 0\\) \\(\circ\\ 5x \geq 0\\) \\(\circ\\ 5x - 5 \geq 0\\)

Explanation:

Step1: Recall domain of square root

For a square root function $\sqrt{u}$, the expression inside (radicand) $u$ must be non - negative, i.e., $u\geq0$.

Step2: Identify the radicand in $f(x)$

In the function $f(x)=\sqrt{5x - 5}+1$, the radicand is $5x-5$.

Step3: Determine the inequality

To find the domain, we set the radicand greater than or equal to zero. So we use the inequality $5x - 5\geq0$.

Answer:

$5x - 5\geq0$ (corresponding to the option with this inequality)