A real valued function f(x) satisfies the functional equation

f(x - y) = f(x)f(y) - f(a - x)f(a + y)

where a is given constant and f(0) = 1, f(2a - x) is equal to

The range of the function f(x) = $${}^{7 - x}{P_{x - 3}}$$ is

If $$f:R \to S$$, defined by
$$f\left( x \right) = \sin x - \sqrt 3 \cos x + 1$$,
is onto, then the interval of $$S$$ is

The graph of the function y = f(x) is symmetrical about the line x = 2, then