Answer:
See below
Step-by-step explanation:
In an odd function f(-x) will equal -f(x).
An example is f(x) = x^3:-
f(-x) = (-x)^3 and -f(x) = -x^3:-
(-x)^3 = -x * -x * -x = -x^3.
Answer: [tex]f(x)=5x^{3}-x[/tex]
Step-by-step explanation:
1. By definition, algebraically, a function is odd when:
[tex]-f(x)=f(-x)[/tex]
2. Therefore, if you have the following function:
[tex]f(x)=5x^{3}-x[/tex]
You can know if it is odd by substituting [tex]x=-x[/tex]:
[tex]f(-x)=5(-x)^{3}-(-x)[/tex]
[tex]f(-x)=-5x^{3}+x[/tex]
3. [tex]-f(x)[/tex] is:
[tex]-f(x)=-5x^{3}+x[/tex]
4. Then, as [tex]-f(x)=f(-x)[/tex] it is odd
