Question #188348

X3-2x is it odd function or even


1
Expert's answer
2021-05-07T10:21:43-0400

Let f(x)=x32xf(x)=x^3-2x

Require to verify whether the given function f(x)f(x) is even or odd.


Recollect the following:

A function f(x)f(x) is said to be even function if f(x)=f(x)f(-x)=f(x) and

A function f(x)f(x) is said to be odd function if f(x)=f(x)f(-x)=-f(x)


Now f(x)=x32xf(x)=(x)32(x)f(x)=x^3-2x\Rightarrow f(-x)=(-x)^3-2(-x)

f(x)=x3+2x\Rightarrow f(-x)=-x^3+2x

f(x)=(x32x)\Rightarrow f(-x)=-(x^3-2x)

f(x)=f(x)\Rightarrow f(-x)=-f(x)

Therefore, the given function is odd function.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS