Even or odd

Algebra Level 3

Suppose f ( x + a ) = f ( x ) + f ( a ) f(x+a) = f(x)+f(a) , where a a is constant and a , x ∈ R a, x \in \mathbb R . Then is f f even or odd?

Odd function Even function

Akash Shukla by Akash Shukla , 26, India

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2 solutions

Put x = a = 0 x = a = 0
f ( 0 ) = 2 f ( 0 ) f(0) = 2f(0)
f ( 0 ) = 0 f(0) = 0
Put a = − x a = -x
f ( 0 ) = f ( x ) + f ( − x ) f(0) = f(x) + f(-x)
f ( x ) = − f ( − x ) f(x) = -f(-x)
Thus, it is an odd function .

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Ayesha Khan
Jun 30, 2016

To check whether a function is even or odd we put x=-x in the function f(x). Alfter solving if f(x)=f(-x) then the given function is even. f(x)=-f(-x) then the given function is odd.

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