How do you determine if #f(x) = cos^2 x + cos x - 3# is an even or odd function?

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Answer 1 · 2016-07-26T14:05:52

#f# is even .

A given fun. #g# is odd #iff AA x,g(-x)=-g(x)#.

A fun. #g# is even #iff AA x, g(-x)=g(x)#.

Now, for our fun. #f, f(x)=(cosx)^2+cosx-3#

#:. f(-x)=(cos(-x))^2+cos(-x)-3#

But, #cos(-x)=cosx#, hence,

#f(-x)=(cosx)^2+cosx-3=f(x)#

Therefore, #f# is even .