Respuesta :

Answer:

Option 3

Step-by-step explanation:

We are given that

f(x) = 1-x

To find out f(i) we replace x by i

f(i) = 1-i

Thus this is a complex number with real part = 1 and imaginary part =-1

Modulus of f(i) = |1-i| =

[tex]\sqrt{1^2+(-1)^2} \\=\sqrt{2}[/tex]

Thus answer is option C

square root of 2

Answer:

Option C is correct

[tex]\sqrt{2}[/tex]  value is equivalent to |f(i)|

Step-by-step explanation:

Modulus of the complex number z = a+ib is given by:

[tex]|z| = \sqrt{a^2+b^2}[/tex]

As per the statement:

Given the function:

[tex]f(x) = 1-x[/tex]

Substitute x = i we have;

[tex]f(i) = 1-i[/tex]; where, i is the imaginary part.

We have to find |f(i)|.

[tex]|f(i)| = |1-i|[/tex]

By definition of modulus;

[tex]|f(i)| =\sqrt{1^2+(-1)^2}[/tex]

⇒[tex]|f(i)| =\sqrt{1+1}[/tex]

⇒[tex]|f(i)| =\sqrt{2}[/tex]

Therefore, the value of |f(i)| is, [tex]\sqrt{2}[/tex]

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