$X, Y$ are continuous random variables taking values in $[0,1]$. Their joint density is $f(x, y) = x+y$ when $x, y \in [0,1]$, and $f(x,y) = 0$ otherwise.
Is it possible to conclude whether or not $X, Y$ are independent from just this definition without performing any calculations or mathematical manipulation? i.e. just by inspection of the joint pdf. If so, how?