Question

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

A) –2 + i
b) –2 – i
c) 2 + i
d) 2 – i

Answer 1

f(i)=2-i

d is the correct option.

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.

Answer 2

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