Questions: If f(x)=1-x, which value is equivalent to f(x) ? 0 1 √2 √(-1)

Solution Steps

To solve this problem, we need to evaluate the function \( f(x) = 1 - x \) and then find the absolute value of the result. We will test each of the given values to see which one matches the absolute value of \( f(x) \).

1. Define the function \( f(x) = 1 - x \).
2. Calculate \( f(x) \) for each given value.
3. Take the absolute value of the result.
4. Compare the absolute value to the given options to find the equivalent value.

Given the function \( f(x) = 1 - x \), we need to find the value equivalent to \( |f(x)| \).

First, let's evaluate \( f(x) \): \[ f(x) = 1 - x \]

Next, we apply the absolute value to \( f(x) \): \[ |f(x)| = |1 - x| \]

We need to determine which of the given options is equivalent to \( |1 - x| \):

• 0
• 1
• \( \sqrt{2} \)
• \( \sqrt{-1} \)

1. Option 0: \( |1 - x| \) can be 0 if \( x = 1 \). This is a possible value.
2. Option 1: \( |1 - x| \) can be 1 if \( x = 0 \) or \( x = 2 \). This is also a possible value.
3. Option \( \sqrt{2} \): \( |1 - x| \) can be \( \sqrt{2} \) if \( x = 1 - \sqrt{2} \) or \( x = 1 + \sqrt{2} \). This is a possible value.
4. Option \( \sqrt{-1} \): \( \sqrt{-1} \) is an imaginary number (i), and the absolute value function \( |1 - x| \) cannot be imaginary. This is not a possible value.

Final Answer