# Which statement best describes how to determine whether f(x) = x^{4} - x^{3} is an even function?

**Solution:**

Functions can be even, odd, both, or neither of them.

A function is even if f(x) = f(-x) for all x and a function is odd if -f(x) = f(-x) for all x.

Here f(x) = x^{4} - x^{3}

⇒ f(-x) = (-x)^{4} - (-x)^{3} = x^{4 }- (-x^{3}) = x^{4} + x^{3}

So, f( -x) is not equal to f(x) or -f(x).

Hence, f(x) is neither even nor an odd function.

Thus, we have seen the nature of even function and ways to determine the nature of the function.

## Which statement best describes how to determine whether f(x) = x^{4} - x^{3} is an even function?

**Summary:**

The statement best describes how to determine whether f(x) = x^{4} - x^{3} is an even function is "A function is even if f(x) = f(-x) for all x."

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