What can be said about the sum and difference of each pair of functions? (a) Two even functions (b) Two odd functions (c) An odd function and an even function

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What can be said about the sum and difference of each pair of functions?     (a) Two even functions     (b) Two odd functions     (c) An odd function and an even function

jlo2niT · Accepted Answer

Step 1 (a) Let f{(x}) be an even function and g{(x}) be also an even function. Since, by the property of an even function we know that f{(−x})=f{(x}) and g{(−x})=g{(x}). Now, cos idering the sum h{(x})={(x})+g{(x}) h{(−x})=f{(−x})+g{(−x})=f{(x})+g{(x}) ⇒h{(−x})=h{(x}) Hence, we can conclude that the sum of two even functions is an even function. Considering the difference, h{(x})=f{(x})−g{(x}) h{(−x})=f{(−x})−g{(−x}) ⇒h{(−x})=f{(x})−g{(x})=h{(x}) Hence, the difference of two even functions are even functions.

What can be said about the sum and difference of

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