I just mentally put one of the x's on the right under the y, put the other under the radical, saw that it was now a function only in terms of y/x and had the answer in about 5 seconds.
Everybody so far is wrong. The original function as written as ambiguous because it has two different values for F of -2. Depending on if y is negative or if X is negative, the result could either be positive or negative.
I went the trig route as y/x is the slope of a hypotenuse of length sqrt(x^2+y^2) Gives f(x) = x sec(arctan x) And an obscure identity later yields the same result
These seem dangerous and hard to know if there even is a solution without checking. If f(x+y)=x^2+y^2, then f(1+1)=2 but f(2+0)=4. Method 1 suggests that your kind of f must be constant along lines y=mx, and so the x's should cancel from the right, since there are no x's on the left.
shouldn't the answer be f(x) = +-x*sqrt(x^2+1) the original equation is: f(x, y) = y*sqrt(x^2 + y^2)/x^2 "x" doesn't actually appear anywhere by itself, only "x^2" but y does appear by itself f(2/2) = f(1) = 2*sqrt(4 + 4)/4 = sqrt2 but f(-2/-2) = f(1) = -2*sqrt(4 + 4)/4 = -sqrt2