Which statement best describes how to determine whether f(x) = x⁴ - x³ 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) = x⁴ - x³

⇒ f(-x) = (-x)⁴ - (-x)³ = x⁴ - (-x³) = x⁴ + x³

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) = x⁴ - x³ is an even function?

Summary:

The statement best describes how to determine whether f(x) = x⁴ - x³ is an even function is "A function is even if f(x) = f(-x) for all x."