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