Answer
Neither odd nor even.
Work Step by Step
We know that if a function is odd, then $f(-x)=-f(x).$
We know that if a function is even, then $f(-x)=f(x).$
Hence we plug in $-x$ to see what happens.
$f(-x)=\frac{(-x)^2}{2(-x)+1}=\frac{x^2}{-2x+1}\ne f(x)\ne-f(x).$ Therefore the function is neither odd nor even.
