If f(x) = 4x $$-$$ x², x$$\in$$R, and f(a + 1) $$-$$ f(a $$-$$ 1) = 0, then a is equal to

The maximum value of the function y = x(x $$-$$ 1)², is

Find the area enclosed by the loop in the curve 4y² = 4x² $$-$$ x³.

If $$2f(xy) = {(f(x))^x} + {(f(y))^x}$$ for all $$x,y \in R$$ and $$f(1) = a( \ne 1)$$. Then $$\sum\limits_{k = 1}^n {f(k) = } $$