Answer:
f(-x)= -f(x) so, the given function [tex]f(x)= x^3-2x[/tex] is Odd
Step-by-step explanation:
We need to determine if the function [tex]f(x)= x^3-2x[/tex] is Even, Odd, or Neither.
Determining if a function f(x) is even or not we put x=-x and check
If f(-x)=f(x) the function is even
if f(-x)= -f(x) the function is odd
So, Putting x =-x and determining if the given function [tex]f(x)= x^3-2x[/tex] is Even, Odd, or Neither.
[tex]f(x)= x^3-2x\\Put \ x=-x\\f(-x)=(-x)^3-2(-x)\\f(-x)=-x^3+2x\\f(-x)=-(x^3-2x)\\f(-x)=-f(x)[/tex]
As f(-x)= -f(x) so, the given function [tex]f(x)= x^3-2x[/tex] is Odd
