Answer to Question #308086 in Calculus for Voice maker

Question #308086

Question 5 [2;2]


Investigate whether the following functions are odd or even.


(a) 𝑓(π‘₯) = π‘₯^


3


(b) 𝑓(π‘₯) = cos π‘₯

1
Expert's answer
2022-03-10T08:41:06-0500

A function is even if f(βˆ’x)=f(x)f(-x)=f(x)


A function is odd if f(βˆ’x)=βˆ’f(x)f(-x)=-f(x)


1.

f(x)=xΒ³f(x)=xΒ³


f(βˆ’x)=(βˆ’x)Β³=βˆ’xΒ³=βˆ’f(x)f(-x)=(-x)Β³=-xΒ³=-f(x)


Hence, f(x)=xΒ³f(x)=xΒ³ is an odd function


2.

f(x)=cosxf(x)=cosx


f(βˆ’x)=cos(βˆ’x)=cosx=f(x)f(-x)=cos(-x)=cosx=f(x)


Hence, f(x)=cosxf(x)=cosx is an even function



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