Question

on $f(x) = \sqrt{5x - 5} + 1$.
used to find the domain?\t\twhat is the domain of the function?
\t\t\tdomain: $x$
\t\t\tdone
\t\t\t-5
\t\t\t-1
\t\t\t1
\t\t\t5

Explanation:

Step1: Determine the condition for the square root

For the function \( f(x)=\sqrt{5x - 5}+1 \), the expression inside the square root (the radicand) must be non - negative. So we set up the inequality \( 5x-5\geq0 \).

Step2: Solve the inequality

Add 5 to both sides of the inequality \( 5x - 5\geq0 \):
\( 5x-5 + 5\geq0 + 5 \)
\( 5x\geq5 \)
Divide both sides by 5:
\( \frac{5x}{5}\geq\frac{5}{5} \)
\( x\geq1 \)

Answer:

The domain of the function \( f(x)=\sqrt{5x - 5}+1 \) is \( x\geq1 \), so the correct symbol is \( \geq \) and the number is \( 1 \).