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How do you know if #g(x)= sin x + cos x# is an even or odd function?

Answer 1

Elijah Allen

I would say neither even nor odd:

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Answer 2

Serenity Johnson

To determine if ( g(x) = \sin(x) + \cos(x) ) is an even or odd function, we can use the properties of even and odd functions.

An even function satisfies the property ( f(-x) = f(x) ) for all ( x ) in its domain. An odd function satisfies the property ( f(-x) = -f(x) ) for all ( x ) in its domain.

For ( g(x) = \sin(x) + \cos(x) ):

( g(-x) = \sin(-x) + \cos(-x) )
( g(-x) = -\sin(x) + \cos(x) )

Comparing this to ( g(x) ), which is ( \sin(x) + \cos(x) ), we can see that ( g(-x) ) is equal to ( -g(x) ).

Since ( g(-x) = -g(x) ), ( g(x) = \sin(x) + \cos(x) ) is an odd function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.