Let f : R $$ \to $$ R be a function defined by
f(x) = max {x, x²}. Let S denote the set of all points in R, where f is not differentiable. Then :

For all twice differentiable functions f : R $$ \to $$ R,
with f(0) = f(1) = f'(0) = 0

The integral $$\int\limits_1^2 {{e^x}.{x^x}\left( {2 + {{\log }_e}x} \right)} dx$$ equals :

For a suitably chosen real constant a, let a

function, $$f:R - \left\{ { - a} \right\} \to R$$ be defined by

$$f(x) = {{a - x} \over {a + x}}$$. Further suppose that for any real number $$x \ne - a$$ and $$f(x) \ne - a$$,

(fof)(x) = x. Then $$f\left( { - {1 \over 2}} \right)$$ is equal to :