Precalculus Textbook 8th Edition Section 2.2 Exercise 56 Solution
Question:
If n is an integer n >=1, prove that f(x) = xn is an odd function if n is odd and is an even function if n is even.
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Solution:
Given function is f(x) = xn.
Case 1: If n is an odd number, Then put -x in place of x.
f(-x) = (-x)n = -xn = -f(x).
Thus, f(x) is an ODD function.
Case 2: If n is an even number, Then put -x in place of x.
f(-x) = (-x)n = xn = f(x).
Thus, f(x) is an EVEN function.
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