Answer:
The correct option is 3. The function f(x) is even.
Step-by-step explanation:
The given function is
[tex]f(x)=-2x^4+3x^2[/tex]
A function is called an even function if
[tex]f(-x)=f(x)[/tex]
A function is called an odd function if
[tex]f(-x)=-f(x)[/tex]
Substitute x=-x in the given function.
[tex]f(-x)=-2(-x)^4+3(-x)^2[/tex]
[tex]f(-x)=-2x^4+3x^2[/tex]
[tex]f(-x)=f(x)[/tex]
Function f(x) is an even function.
Therefore option 3 is correct.
