When you add or subtract two even functions, what type of function will you get?

1 Answer
George C.
Oct 18, 2015

It will always be an even function.

Explanation:

Suppose #f(x)# and #g(x)# are both even.

Then by definition #f(-x) = f(x)# and #g(-x) = g(x)# for all #x# in the domain.

So if #h(x) = f(x)+g(x)# and #j(x) = f(x)-g(x)# then

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

#j(-x) = f(-x)-g(-x) = f(x)-g(x) = j(x)#

So both #h(x)# and #j(x)# satisfy the condition for being even functions.

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