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

Solution:

Given function f(x) = x³ - 2x²

i² = -1, where i = imaginary number

Put x = i [i = √-1] in the given function.

If f(x) = x³ - 2x² , then 

⇒ f(i) = i³ - 2i²

⇒ f(i) = (√-1)³ - 2(√-1)² 

⇒ f(i) = (√-1)²(√-1) - 2(-1)

⇒ f(i) = -1(i) + 2 = 2 - i

⇒ f(i) = 2 - i

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

Summary:

The value of f(i) will be 2 - i when f(x) = x³ - 2x².