Question: Find the values p(3), p(9), p(11) and p(0) for the function, if they exist.
p(z) = \sqrt{2z - 18}
Find p(3). Select the correct choice and, if necessary, fill in the answer box within your choice.
A. p(3) = [ ]
(Simplify your answer. Type an exact answer using radicals as needed.)
B. The function value does not exist. The square root does not have a real number solution.
1. **State the problem:** We need to find the value of the function $$p(z) = \sqrt{2z - 18}$$ at $$z=3$$.
2. **Substitute the value:** Substitute $$z=3$$ into the function:
$$p(3) = \sqrt{2(3) - 18}$$
3. **Simplify inside the square root:**
$$p(3) = \sqrt{6 - 18} = \sqrt{-12}$$
4. **Check if the value inside the square root is non-negative:** Since $$-12 < 0$$, the square root of a negative number is not a real number.
5. **Conclusion:** The function value $$p(3)$$ does not exist in the real numbers because the square root of a negative number is not defined for real values.
**Final answer:**
$$\boxed{\text{The function value does not exist.}}$$