Consider the functions E and O of Exercises 1 and 2.
a) Show that f(x)= E(x)+ O(x). This means that every function can be expressed as the sum of an even function and an odd function.
b) Let f(x) = 4x3 − 11x2 + − 10. Expressf as a sum of an even function and an odd function.
Exercises 1
Show that iff is any function, then the function E defined by is even.
Exercises 2
Show that iff is any function, then the function O defined by is odd.
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