Neither Odd Nor Even?
Algebra
Level
3
How many function(s) with domain
and range
are both even and odd?
Image Credit: Wikipedia Even and Odd Function
Infinitely many
2
1
0
Greater than 2
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1 solution
An even function satisfies
f ( − x ) = f ( x )
for all x in the domain. An odd function satisfies
f ( − x ) = − f ( x )
for all x in the domain. Thus, a function that is both even and odd must have
f ( x ) = − f ( x ) .
The only function with range in the real numbers that satisfies this is f ( x ) = 0 , so there is only 1 function.