A function is defined by the equatino `f (x) = (x ^(2))/(4) - 11.` For this function, which of the following domain values corresponds to a range value of 14 ?

Options

A. `-4`
B. 10
C. 38
D. 100

Explanation

To find the domain values that correspond to a range value of 14 for the function \( f(x) = \frac{x^2}{4} - 11 \), we can follow these steps:

### Step-by-Step Solution:

1. **Set the function equal to the desired range value**:
\[ f(x) = 14 \]
Thus, we have:
\[ \frac{x^2}{4} - 11 = 14 \]

2. **Add 11 to both sides**:
\[ \frac{x^2}{4} = 14 + 11 \]
Simplifying the right side gives:
\[ \frac{x^2}{4} = 25 \]

3. **Multiply both sides by 4** to eliminate the fraction:
\[ x^2 = 25 \times 4 \]
This simplifies to:
\[ x^2 = 100 \]

4. **Take the square root of both sides**:
\[ x = \pm \sqrt{100} \]
Therefore, we find:
\[ x = \pm 10 \]

5. **Identify the domain values**:
The domain values that correspond to the range value of 14 are:
\[ x = 10 \quad \text{and} \quad x = -10 \]

### Final Answer:
The domain values corresponding to a range value of 14 are \( x = 10 \) and \( x = -10 \). If only positive values are considered, then the answer is \( x = 10 \).