Domain of the function $f(x)\,=\,\frac{1}{{\sqrt {(x + 1)({e^x} - 1)(x - 4)(x + 5)(x - 6)} }}$
$( - \infty , - 5) \cup ( - 1,4) \cup (6,8)$
$( - \infty , - 5) \cup ( - 1,0) \cup (0,4) \cup (6,\infty )$
$( - 5, - 1) \cup (0,4) \cup (6,\infty )$
$( - \infty , - 5) \cup ( - 1,4) \cup [6,\infty )$
If $f\left( x \right) + 2f\left( {\frac{1}{x}} \right) = 3x,x \ne 0$ and $S = \left\{ {x \in R:f\left( x \right) = f\left( { - x} \right)} \right\}$;then $S :$
If $y = 3[x] + 1 = 4[x -1] -10$, then $[x + 2y]$ is equal to (where $[.]$ is $G.I.F.$)
Let $f(x) = (1 + {b^2}){x^2} + 2bx + 1$ and $m(b)$ the minimum value of $f(x)$ for a given $b$. As $b$ varies, the range of $m(b)$ is
Let $f : R \rightarrow R$ be a continuous function such that $f(3 x)-f(x)=x$. If $f(8)=7$, then $f(14)$ is equal to.