Question

Which of the following is an odd function

Answer 1

Given the functions

(a) f(x) = x³ + 5x² + x

(b) f(x) = x² + x

(c) f(x) = -x

Function (a)

f(-x) = (-x)³ + 5(-x)² + (-x)  

      = -x³ + 5x² - x

      = -(x³ - 5x² + x)

The function is neither even nor odd.

Function (b)

f(-x) = (-x)² + (-x)

       = -(-x² + x)

The function is neither even nor odd.

Function (c)

f(-x) = -(-x)  

      = x

      = -f(x)

Because f(-x) = -f(x) the function is odd.

Answer: f(x) = -x is an odd function.