Which Statement Best Describes How to Determine Whether f(x) = 9 – 4x^2 is an Odd Function?


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

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

Answer: Here f(x) = f(−x). So, f(x) = 9 – 4xis not an odd function. In fact f(x) = 9 – 4xis an even function.

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.

Explanation:

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 xis an even function, 4xis 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.