Domain of the function $f(x) = \frac{{{x^2} - 3x + 2}}{{{x^2} + x - 6}}$ is
$\{ x:x \in R,\;\;x \ne 3\} $
$\{ x:x \in R,\;\;x \ne 2\} $
$\{ x:x \in R\} $
$\{ x:x \in R,\;\;x \ne 2,\;x \ne - 3\} $
Let $a,b,c\; \in R.$ If $f\left( x \right) = a{x^2} + bx + c$ is such that $a + b + c = 3$ and $f\left( {x + y} \right) = f\left( x \right) + f\left( y \right) + xy,$ $\forall x,y \in R,$ then $\mathop \sum \limits_{n = 1}^{10} f\left( n \right)$ is equal to :
If the function $f\,:\,R - \,\{ 1, - 1\} \to A$ defined by $f\,(x)\, = \frac{{{x^2}}}{{1 - {x^2}}},$ is surjective, then $A$ is equal to
The function $f$ satisfies the functional equation $3f(x) + 2f\left( {\frac{{x + 59}}{{x - 1}}} \right) = 10x + 30$ for all real $x \ne 1$. The value of $f(7)$ is
If $f(x) = \cos (\log x)$, then $f(x)f(y) - \frac{1}{2}[f(x/y) + f(xy)] = $
The value of $\sum \limits_{n=0}^{1947} \frac{1}{2^n+\sqrt{2^{1994}}}$ is equal to