SOLUTION: Prove that if f(x) and g(x) are both even functions, then h(x) = f(x) + g(x) is an even function.
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Question 980559: Prove that if f(x) and g(x) are both even functions, then h(x) = f(x) + g(x) is an even function.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ f(-x)\ \ \ \ \ \ )
Definition of even function
\ =\ g(-x)\ \ \ \ \ \ )
Definition of even function
\ +\ g(x)\ =\ f(-x)\ +\ g(-x)\ \ \ \ \ \ )
Addition property of Equality
\ =\ f(-x)\ +\ g(-x)\ \ \ \ \ \ )
Definition )
\ =\ h(-x)\ \ \ \ \ \)
Substitution
is even by definition of even function. Q.E.D.
John
My calculator said it, I believe it, that settles it
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