Question

A function f(x) is even, 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)

This question was addressed to me during an interview.

Enquiry is from Channel in portion Elements of Communication System of Analog Communications

Answer 1

The correct answer is (b) f(x) = f(-x)

For explanation 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).