The problem asks us to find the domain of the function $f(x) = \sqrt{3x+5}$.

1. Problem Description

The problem asks us to find the domain of the function $f(x) = \sqrt{3x+5}$.

2. Solution Steps

The domain of a square root function is the set of all real numbers for which the expression inside the square root is greater than or equal to zero. Therefore, we need to solve the inequality $3x+5 \ge 0$.

$3x + 5 \ge 0$

$3x \ge -5$

$x \ge -\frac{5}{3}$

Thus, the domain of the function is all real numbers $x$ such that $x \ge -\frac{5}{3}$.

3. Final Answer

The final answer is d) All real numbers where $x \ge -\frac{5}{3}$.