Let $$f(n) = \left[ {{1 \over 4} + {n \over {1000}}} \right]$$, where [x] denote the integral part of x. Then the value of $$\sum\limits_{n = 1}^{1000} {f(n)} $$ is

If $$f(x) = {{4x + {x^4}} \over {1 + 4{x^3}}}$$ and $$g(x) = \ln \left( {{{1 + x} \over {1 - x}}} \right)$$, then what is the value of $$(fog)\left( {{{e - 1} \over {e + 1}}} \right)$$ equal to ?

If $$f(x) = {x \over {x - 1}}$$, then what is $${{f(a)} \over {f(a + 1)}}$$ equal to ?

Let f : [$$-$$6, 6] $$\to$$ R be defined by f(x) = x² $$-$$ 3. Considered the following :

1. $$(f \circ f \circ f)( - 1) = (f \circ f \circ f)(1)$$

2. $$(f \circ f \circ f)( - 1) - 4(f \circ f \circ f)(1)$$

$$ = (f \circ f)(0)$$

Which of the above is/are correct?