1.

Find an if the function f(x) = x - x³.​

Answer»

Answer:

The function f(X) is odd, if:

f(−x)=−f(x)

and EVEN, if:

f(−x)=f(x)

Given that

f(x)=∣x∣−x

3

f(−x)=∣−x∣−(−x)

3

=∣−x∣+x

3

Since ∣x∣ is an even function,

∣−x∣=∣x∣

∴f(−x)=∣x∣+x

3

Also,

−f(x)=−∣x∣+x

3

Hence,

f(−x)

=f(x)

and

f(−x)

=−f(x)

f(x) is neither odd nor even


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