Respuesta :

jessicashea02
f(x)=f(-x) definition of even function
g(x)=g(-x) definition of even function
f(x)+g(x)=f(-x)+g(-x)  Addition property of equality
h(-x)=f(-x)+g(-x) Definition h(x)
h(x)=h(-x)  Substitution
h(x) is even by definition of even function
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botellok

Answer:

yes, it is.

Step-by-step explanation:

An even function is that where for any x, f(-x)=-f(x).

So, suppose that f(x) and g(x) are even functions and define h(x)= f(x)+g(x). Then:

h(-x) = f(-x)+g(-x)

= -f(x)+(-g(x)) because f and g are even functions.

= -f(x)-g(x)

= -(f(x)+g(x))

= -h(x).

Then, h(x) is an even function.

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