Question: Find the indicated values for the function $f(x) = \sqrt{5x - 25}$.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $f(9) = 4.47$ (Round to the nearest hundredth as needed.)
B. The function value is not a real number.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $f(5) = 0$ (Round to the nearest hundredth as needed.)
B. The function value is not a real number.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $f(2) =$ (Round to the nearest hundredth as needed.)
B. The function value is not a real number.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $f(-2) =$ (Round to the nearest hundredth as needed.)
B. The function value is not a real number.
1. **State the problem:** We need to find the values of the function $f(x) = \sqrt{5x - 25}$ at $x=9$, $x=5$, $x=2$, and $x=-2$.
2. **Recall the domain rule for square root functions:** The expression inside the square root must be greater than or equal to zero for the function to have real values. That is,
$$5x - 25 \geq 0$$
3. **Solve the domain inequality:**
$$5x - 25 \geq 0$$
$$5x \geq 25$$
$$x \geq 5$$
So, the function is defined for $x \geq 5$.
4. **Evaluate $f(9)$:**
$$f(9) = \sqrt{5(9) - 25} = \sqrt{45 - 25} = \sqrt{20}$$
Simplify and round:
$$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5} \approx 4.4721 \approx 4.47$$
5. **Evaluate $f(5)$:**
$$f(5) = \sqrt{5(5) - 25} = \sqrt{25 - 25} = \sqrt{0} = 0$$
6. **Evaluate $f(2)$:**
Check domain first: $2 < 5$, so inside the root is negative.
$$5(2) - 25 = 10 - 25 = -15 < 0$$
Therefore, $f(2)$ is not a real number.
7. **Evaluate $f(-2)$:**
Check domain first: $-2 < 5$, so inside the root is negative.
$$5(-2) - 25 = -10 - 25 = -35 < 0$$
Therefore, $f(-2)$ is not a real number.
**Final answers:**
- $f(9) \approx 4.47$
- $f(5) = 0$
- $f(2)$ is not a real number
- $f(-2)$ is not a real number