f(x)=cos(x) and g(x)=sin(x) what is fOg is it even,odd or neither?

Question

anonymous · Answer

fOg = cos(sin(x))

anonymous · Answer

cos is outside.. so it should be even

amistre64 · Answer

should be, but there must be a way to test it out :)

hartnn · Answer

yup, if fog(x) = fog(-x)
then it is even
yup, if fog(x) =- fog(-x)
then it is odd
else neither
so just replace x by -x in fog(x) and find it out

ghazi · Answer

sin(-x)=- sin x and cos(-x)= cos x....hope this helps you

ghazi · Answer

fog = cos(sin(x))

ghazi · Answer

$$\cos(\sin(-x))=\cos(-\sin x)=\cos(\sin x)$$

ghazi · Answer

does it look like f(-x)=f(x) now match this with the statement given by @hartnn  you'll have your answer

hartnn · Answer

u almost did all the work for him/her

ghazi · Answer

because he wasn't doin anything even after lot of hint..sorry for that

anonymous · Answer

yes i already had that answer F(X) = cos(sin(x)) but it still not clear whether it is odd, even or neither

ghazi · Answer

if f(-x)=f(x) then it is even