If length of tangent at any point on the curve $$y = f(x)$$ intercepted between the point and the X-axis is of length 1. Find the equation of the curve.

Find the area bounded by the curves $$x^{2}=y, x^{2}=-y$$ and $$y^{2}=4 x-3$$.

If one of the vertices of the square circumscribing the circle $$|z-1|=\sqrt{2}$$ is $$(2+\sqrt{3 i})$$. Find the other vertices of square.

If $$f(x-y)=f(x) \circ g(y)-f(y) \circ g(x)$$ And $$g(x-y) =g(x) \circ g(y)+f(x) \circ f(y)$$ for all $$x, y \in \mathrm{R}$$. If right-hand derivative at $$x=0$$ exists for $$f(x)$$, find the derivative of $$g(x)$$ at $$x=0$$