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Q.) Which of the following functions is an odd function?

a) ${ 2 }^{ -X*X }$

b) ${ 2 }^{ X*-X*X*X*X }$

c)Both (a) and (b)

(d) Neither (a) nor (b)

Solution :

For any function to be an Odd Function , It must satisfy the following condition

f(X) = -f(-X)

Option(a)

f(X) = ${ 2 }^{ -X*X }$

f(-X) = ${ 2 }^{ -(-X)*(-X) }$ = ${ 2 }^{ X*(-X) }$ = f(X)

So, Option(a) is not Odd Function

Option(b)

f(X) = ${ 2 }^{ X*-X*X*X*X }$

f(-X) = ${ 2 }^{ (-X)*-(-X)*(-X)*(-X)*(-X) }$ = ${ 2 }^{ -X*X*-X*-X*-X }$ = ${ 2 }^{ X*X*X*X*X }$ which is not equal to f(-X).

So, Option(b) is also not Odd Function.

Hence , Option(d) i.e. Neither (a) not (b) is Odd Function.