Define Even and odd Function?

1.	Define Even and odd Function?
Answer» • If f (x) is a function of x such that f (– x) = f (x) for every x ∈ domain, then f (x) is an even function of x. Ex. (i) f (x) = cos x is an even function as f (– x) = cos (– x) = cos x = f (x) (ii) f (x) = x⁴ + 2 is an even function as f (– x) = (– x)⁴ + 2 = x⁴ + 2 = f (x). • If f (x) is a function of x such that f (– x) = – f (x) for every x ∈ domain, then f (x) is an odd function of x. Ex. (i) f (x) = sin x is an odd function as f (– x) = sin (– x) = – sin x = – f (x) (ii) f (x) = x³ + 6x is an odd function as f (– x) = (– x)³ + 6(– x) = – x³ – 6x = – (x³+ 6x) = – f (x) • Some functions as y = x²– 5x + 3 are neither even nor odd.

Answer»

• If f (x) is a function of x such that f (– x) = f (x) for every x ∈ domain, then f (x) is an even function of x.

Ex.

(i) f (x) = cos x is an even function as f (– x) = cos (– x) = cos x = f (x)

(ii) f (x) = x⁴ + 2 is an even function as f (– x) = (– x)⁴ + 2 = x⁴ + 2 = f (x).

• If f (x) is a function of x such that f (– x) = – f (x) for every x ∈ domain, then f (x) is an odd function of x.

Ex.

(i) f (x) = sin x is an odd function as f (– x) = sin (– x) = – sin x = – f (x)

(ii) f (x) = x³ + 6x is an odd function as f (– x) = (– x)³ + 6(– x) = – x³ – 6x

= – (x³+ 6x) = – f (x)

• Some functions as y = x²– 5x + 3 are neither even nor odd.

Discussion