# Determine algebraically whether the given function is even, odd, or neither: f(x) = x^{5} - x^{3} + x.

Functions are very important concepts in mathematics. There are many types of functions, which include even functions, odd functions, or neither odd nor even functions.

### Answer: The function f(x) = x^{5} - x^{3} + x is an odd function.

Let's understand the solution in detail.

**Explanation:**

To check for odd functions, we have to verify whether f(-x) = -f(x).

We have f(x) = x^{5} - x^{3} + x.

Now, we find f(-x):

f(-x) = (-x)^{5} - (-x)^{3} + (-x)

f(-x) = -x^{5} + x^{3} - x

Now, we find -f(x):

-f(x) = -(x^{5} - x^{3} + x)

-f(x) = -x^{5} + x^{3} - x

Hence, we see that f(-x) = -f(x)

### Thus, we conclude that the given function f(x) = x^{5} - x^{3} + x is an odd function.

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