Answer:
The function f(x) is neither even, nor odd function.
Step-by-step explanation:
Definition: A function is called an even function if for all x from its domain
[tex]f(-x)=f(x)[/tex]
Definition: A function is called an odd function if for all x from its domain
[tex]f(-x)=-f(x)[/tex]
You are given the function [tex]f(x)=-x^3-2x^2+5.[/tex]
Substitute into the function expression -x instead of x.
[tex]f(-x)=-(-x)^3-2(-x)^2+5\\ \\f(-x)=-(-x^3)-2x^2+5=x^3-2x^2+5\neq f(x)\\ \\-f(x)=-(-x^3-2x^2+5)=x^3+2x^2-5\\ \\f(-x)\neq -f(x)[/tex]
Hence, the function f(x) is neither even, nor odd function.
