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For a signum function f(x), the value of...

For a signum function f(x), the value of f(x) at x = -4 is

A

`-1`

B

0

C

`-4`

D

4

Text Solution

AI Generated Solution

The correct Answer is:
To find the value of the signum function \( f(x) \) at \( x = -4 \), we can follow these steps: ### Step 1: Understand the Signum Function The signum function, denoted as \( f(x) \), is defined as follows: - \( f(x) = 1 \) if \( x > 0 \) - \( f(x) = 0 \) if \( x = 0 \) - \( f(x) = -1 \) if \( x < 0 \) ### Step 2: Determine the Value of \( x \) We are given \( x = -4 \). We need to determine which condition of the signum function applies to \( x = -4 \). ### Step 3: Check the Condition Since \( -4 \) is less than \( 0 \) (i.e., \( -4 < 0 \)), we use the third condition of the signum function. ### Step 4: Apply the Definition According to the definition of the signum function: - Since \( x < 0 \), we have \( f(-4) = -1 \). ### Conclusion Thus, the value of \( f(x) \) at \( x = -4 \) is \( -1 \). ### Final Answer The value of \( f(-4) \) is \( -1 \). ---
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