Question

If f(x) = x3 – 2x2, which expression is equivalent to f(i)?

Answer 1

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

Answer 2

Answer:

f(i)=2-i

d is the correct option.

Step-by-step explanation:

The given function is $f(x)=x^3-2x^2$

Substitute x = i, to find f(i)

$f(i)=i^3-2(i)^2$

We can rewrite this as

$f(i)=i^2\cdot i-2(i)^2$

Now, we know that $i^2=-1$. Thus, we have

$f(i)=(-1)\cdot i-2(-1)$

On simplifying, we get

$f(i)=-i+2\\\\f(i)=2-i$

d is the correct option.