Question

A function f(x) is odd, when?

(a) f(x) = -f(x)

(b) f(x) = f(-x)

(c) f(x) = -f(x)f(-x)

(d) f(x) = f(x)f(-x)

I got this question in quiz.

Enquiry is from RF Mixing in division Receivers & Transducers of Analog Communications

Answer 1

Correct option is (a) f(x) = -f(x)

To explain I would say: Geometrically a function f(x) is even, if plot of the function is symmetric over y-axis. Algebraically, for any function f(x) to be even, f(x) = f(-x).

While for a function f(x) to be odd, f(x) = -f(-x).