Certainly! Let's solve the problem step-by-step.
First, we are given the function [tex]\( f(x) = 1 - x \)[/tex], and we need to find the value of [tex]\( |f(i)| \)[/tex], where [tex]\( i \)[/tex] is the imaginary unit such that [tex]\( i = \sqrt{-1} \)[/tex].
1. Substitute [tex]\( x = i \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(i) = 1 - i
\][/tex]
2. Calculate the magnitude of the complex number [tex]\( 1 - i \)[/tex]:
The magnitude (or modulus) of a complex number [tex]\( a + bi \)[/tex] is given by [tex]\( \sqrt{a^2 + b^2} \)[/tex].
For the complex number [tex]\( 1 - i \)[/tex], [tex]\( a = 1 \)[/tex] and [tex]\( b = -1 \)[/tex].
3. Compute [tex]\( a^2 + b^2 \)[/tex]:
[tex]\[
a^2 + b^2 = 1^2 + (-1)^2 = 1 + 1 = 2
\][/tex]
4. Take the square root of the result:
[tex]\[
\sqrt{2}
\][/tex]
Therefore, the magnitude [tex]\( |1 - i| \)[/tex] is [tex]\( \sqrt{2} \)[/tex].
So, the value equivalent to [tex]\( |f(i)| \)[/tex] is [tex]\( \sqrt{2} \)[/tex].
The correct answer is:
[tex]\[
\sqrt{2}
\][/tex]
