If the range of $f(x) = \frac{2x^4-14x^2-8x+49}{x^4-7x^2-4x+23}$ is $(a, b]$,then $(a + b)$ is

The domain of the function $f(x) = \frac{\cot^{-1} x}{\sqrt{x^2 - [x^2]}}$,where $[x]$ denotes the greatest integer not greater than $x$,is :

Given that $a, b$ and $c$ are real numbers such that $b^2 = 4ac$ and $a > 0$. The maximal possible set $D \subseteq R$ on which the function $f: D \rightarrow R$ given by $f(x) = \log \{ax^3 + (a+b)x^2 + (b+c)x + c\}$ is defined,is

The domain of the definition of the function $y(x)$ given by the equation $2^x+2^y=2$ is

Let $f(x) = \frac{1}{7 - \sin 5x}$ be a function defined on $R$. Then the range of the function $f(x)$ is equal to:

The domain of the definition of the function $f(x) = \frac{1}{4-x^2} + \log_{10}(x^3-x)$ is