Question

Please help.. Which statement best describes how to determine whether f(x) = 9 – 4x^2 is an odd function?

Determine whether 9 – 4(–x)^2 is equivalent to 9 – 4x^2.

Determine whether 9 – 4(–x^2) is equivalent to 9 + 4x^2.
Determine whether 9 – 4(–x)^2 is equivalent to –(9 – 4x^2).

Determine whether 9 – 4(–x^2) is equivalent to –(9 + 4x^2).

Answer 1

A function \(f\) is odd if and only if \(f(-x) = -f(x)\)

Answer 2

The definition of a odd function is f(-x)=-f(x) & the definition of an even function is f(-x)=f(x). All other cases are considered neither.
What does it mean??

This means if you check the input value for a odd function, lets say F(5), and has some value A. If you put in F(-5) you will get -A. So there is a symmetry about odd function. This is similar for even functions except you will find it would A again, so it has a different kind of symmetry.

Answer 3

\(f(-x) = 9-4(-x)^2\) so then what is \(-f(x)\)????
well \(f(x) = 9-4x^2 \) so \(-f(x) = -(9-4x^2)= \ ?\)

Answer 4

so \(9-4(-x)^2\) would need to equal \(-(9-4x^2) = 4x^2-9\)