Which statement best describes how to determine whether f(x) = 9 - 4x² is an odd function?

Solution:

Functions can be even, odd, both, or neither of them. Let us explore each case in detail.

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.

Given, f(x) = 9 - 4x²

f(-x) = 9 - 4(-x)²

f(-x) = 9 - 4(x²)

f(-x) = 9 - 4x²

Hence, f(x) = f(-x) . So, the given function is an even function.

As x² is an even function, 4x² is also even. Thereby 9 - 4x² is also even.

Thus, f(x) = f(-x) is the determinining statement to decide whether f(x) = 9 - 4x² is an odd function or not.

Which statement best describes how to determine whether f(x) = 9 - 4x² is an odd function?

Summary:

f(x) = f(-x) is the determining statement to decide whether f(x) = 9 - 4x² is an odd function or not.