Question

Consider the function `f(x)= 9x-x^3`. Is this function odd, even, or neither?

Answer 1

odd

Explanation:

odd function`=>f(-x)=-f(x)`

even function`=>f(-x)=f(x)`

`f(x)=9x-x^3`

`f(-x)=9(-x)-(-x)^3`

`f(-x)=-9x- -x^3`

`f(-x)=-9x+x^3`

`f(-x)=-(9x-x^3)=-f(x)`

`:.`odd

Answer 2

`f(x)" is odd"`

Explanation:

To determine if a function f(x) is odd/even

`• "If "f(x)=f(-x)" then " f(x)" is even"`

Even functions are symmetrical about the y-axis.

`• "If "f(-x)=-f(x)" then "f(x)" is odd"`

Odd functions have half-turn symmetry about the origin.

`color(blue)"Test if even"`

`f(-x)=9(-x)-(-x)^3=-9x+x^3`

`"Since "f(x)≠f(-x)" then "f(x)" is not even"`

`color(blue)"Test if odd"`

`-f(x)=-(9x-x^3)=-9x+x^3`

`"Since "f(-x)=-f(x)" then "f(x)" is odd"`
graph{9x-x^3 [-40, 40, -20, 20]}