Determine whether the function is even, odd, or neither: f(x)=x^3 + cosx

Question

hartnn · Answer

put x = -x in f(x)

hartnn · Answer

if f(-x)=f(x) then the function is even

anonymous · Answer

even

hartnn · Answer

if f(-x)=-f(x) then the function is odd

tabithax3 · Answer

@hartnn @ilikephysics2 the back of the book says neither. i don't understand how they got the answer

hartnn · Answer

did u put x= -x
and neither is correct.

hartnn · Answer

what is (-x)^3

tabithax3 · Answer

-x

hartnn · Answer

(-x)^3=-x^3
and whats cos(-x) ?

tabithax3 · Answer

cos(-x)=cosx?

hartnn · Answer

yup, so
f(-x)= -x^3+cos x
now is this f(x) ??
 is this -f(x) ??

anonymous · Answer

oh its cause it crosses the origin with respect to x

anonymous · Answer

do you have a calculator near you?

tabithax3 · Answer

@ilikephysics2 i have both a scientific and graphing calculator with me

anonymous · Answer

graph it and you will see how it is neither it goes throw the x axis and crosses with respect to y

hartnn · Answer

calculator not required,
u got f(-x)= -x^3+cos x
u have f(x)=x^3+cos x
and -f(x)= -x^3-cos x
right? 
so any of these are  equal ??

tabithax3 · Answer

@hartnn i don't think any of them are equal, but i might be wrong?

hartnn · Answer

you are correct, since $f(-x) \ne f(x)$ and $f(-x) \ne -f(x)$
so its neither odd nor even

tabithax3 · Answer

@hartnn thank you for helping, i understand it now :) my professor never explained it in class and my textbook doesn't explain it as well

hartnn · Answer

glad to hear that u understand :)
welcome.