Answer :
Given
[tex]f(x)=-f(x)[/tex]We can sum f(x) on both sides, and we will get
[tex]f(x)+f(x)=-f(x)+f(x)_{}[/tex]But -f(x) + f(x) = 0, then
[tex]f(x)+f(x)=0[/tex]Now we can combine the terms and we get
[tex]2\cdot f(x)=0[/tex]Divide both sides by 2
[tex]f(x)=0[/tex]
And here we have solved our problem. That's the only function that is odd and even at the same time, the graph of this function is basically the x-axis because it's a constant in y = 0, we can see even and odd because
[tex]f(x)=0,\forall x\in\R[/tex]Therefore
[tex]\begin{gathered} f(x)=0=f(-x) \\ \\ f(x)=0=-f(x) \end{gathered}[/tex]Odd and even at the same time.