identify each of the following functions as even, odd, or neither.\na) ( f(x)=x^{3} )\neven\nodd\nneither
identify each of the following functions as even, odd, or neither.\na) ( f(x)=x^{3} )\neven\nodd\nneither
Answer
Explanation:
Step1: Recall the definitions
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.
Step2: Calculate (f(-x))
Given (f(x) = x^{3}), then (f(-x)=(-x)^{3}). Using the rule ((ab)^n=a^nb^n), we have ((-x)^{3}=(-1)^{3}\times x^{3}). Since ((-1)^{3}=-1), so (f(-x)=-x^{3}). And (-f(x)=-(x^{3})=-x^{3}).
Answer:
Odd