How do you determine whether a function is odd, even, or neither: #h(x)= -x^3/(3x^2-9)#?
2 Answers
Jul 20, 2017
Odd
Explanation:
We substitude
Now because
Jul 20, 2017
Explanation:
We use the following condition:
# { (f(-x)=f(x)), (f(-x)=-f(x)) :} => {: (f " is even"), (f " is odd") :}#
So for the given function:
# h(x) = -(x^3)/(3x^2-9) #
And so:
# h(-x) = -((-x)^3)/(3(-x)^2-9) #
# " " = -(-x^3)/(3x^2-9) #
# " " = (x^3)/(3x^2-9) #
# " " = -h(x) #
And we conclude that
We can verify this graphically, as odd functions have rotational symmetry about the origin:
graph{-(x^3)/(3x^2-9) [-20, 20, -10, 10]}