# 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 – 4x^{2} 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 – 4x^{2 }is not an odd function. In fact f(x) = 9 – 4x^{2 }is 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 – 4x^{2}

f(-x) = 9 - 4(-x)^{2}

f(-x) = 9 - 4(x^{2})

f(-x) = 9 – 4x^{2}

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

As x^{2 }is an even function, 4x^{2 }is also even. Thereby 9 – 4x^{2} is also even.

### Thus, f(x) = f(−x) is the determinining statement to decide whether f(x) = 9 – 4x^{2} is an odd function or not.

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