Question

Consider the function f(t) = √(3t - 9). You cannot take the square root of a negative number, so 3t - 9 must be zero. Set up an inequality showing that the radicand cannot be negative. What is the domain of the function?

Answer 1

The domain of the function f(t) = √(3t - 9) is all real numbers t such that t ≥ 3, as the radicand cannot be negative.

Step-by-step explanation:

To determine the domain of the function f(t) = √(3t - 9), we must ensure the radicand (the expression inside the square root) is not negative. The inequality 3t - 9 ≥ 0 must be satisfied for the function to have real number outputs.

By solving the inequality, we add 9 to both sides to obtain 3t ≥ 9. Then, we divide both sides by 3, resulting in t ≥ 3. This means the domain of f(t) is all real numbers t such that t ≥ 3.

The graph of f(t) will start at t = 3 and continue to the right on the number line indefinitely, including all numbers greater than or equal to 3.