If f(x) is a signum function, then f(10) is equal to

Options

A. `-1`
B. 0
C. 1
D. 10

Answer

To solve the problem, we need to evaluate the signum function \( f(x) \) at \( x = 10 \).

### Step-by-Step Solution:

1. **Understand the Signum Function**: The signum function, denoted as \( \text{sgn}(x) \) or \( f(x) \), is defined as follows:
- \( f(x) = -1 \) if \( x < 0 \)
- \( f(x) = 0 \) if \( x = 0 \)
- \( f(x) = 1 \) if \( x > 0 \)

2. **Identify the Value of \( x \)**: In this case, we are given \( x = 10 \).

3. **Determine the Condition**: We need to check which condition of the signum function applies to \( x = 10 \):
- Since \( 10 > 0 \), we fall into the third condition of the signum function.

4. **Evaluate the Function**: According to the definition:
- \( f(10) = 1 \)

5. **Conclusion**: Therefore, the value of \( f(10) \) is \( 1 \).

### Final Answer:
\( f(10) = 1 \)

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