Question

1. choose the domain of the function g(x) = √(x + 5). a) {x|x ≤ -5} b) {x|x ≠ -5} c) {x|x ≥ -5} d) all real numbers

Explanation:

Step1: Recall domain of square root function

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

Step2: Solve the inequality

To solve \( x+5\geq0 \), we subtract 5 from both sides of the inequality.
\( x+5-5\geq0 - 5 \)
Which simplifies to \( x\geq - 5 \).

Answer:

c) \(\{x|x\geq - 5\}\)