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If f(x) = x3 – 2x2, which expression is equivalent to f(i)?
A) –2 + i
b) –2 – i
c) 2 + i
d) 2 – i

Respuesta :

smmwaite

Answer

d) 2 – i


Explanation

f(x) = x³ – 2x²

When x = i, we proceed as follows.

Note: i =

          i² =(√-1)(√-1) =  -1

          i³ = (√-1)(√-1)(√-1) = -1(√-1) = -1i = -i

f(x) = x³ – 2x²

f(i) = i³ – 2i²

     = -i – 2(-1)

     = -i + 2

      = 2 – i


SociometricStar

Answer:

f(i)=2-i

d is the correct option.

Step-by-step explanation:

The given function is [tex]f(x)=x^3-2x^2[/tex]

Substitute x = i, to find f(i)

[tex]f(i)=i^3-2(i)^2[/tex]

We can rewrite this as

[tex]f(i)=i^2\cdot i-2(i)^2[/tex]

Now, we know that [tex]i^2=-1[/tex]. Thus, we have

[tex]f(i)=(-1)\cdot i-2(-1)[/tex]

On simplifying, we get

[tex]f(i)=-i+2\\\\f(i)=2-i[/tex]

d is the correct option.