## Precalculus Textbook 8th Edition Section 2.2 Exercise 56 Solution

**Question**:

If n is an integer n >=1, prove that f(x) = x^{n} 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) = x^{n}.

Case 1: If n is an odd number, Then put -x in place of x.

f(-x) = (-x)^{n} = -x^{n} = -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} = x^{n} = f(x).

Thus, f(x) is an EVEN function.

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