Which one of the following is not bounded on the intervals as indicated
$f(x) =$ ${2^{\frac{1}{{x - 1}}}}$ on $(0, 1)$
$g(x) = x cos \frac{1}{x} $ on $(-\infty ,\infty )$
$h(x) = xe^{-x} $ on $(0, \infty )$
$l (x) =tan^{-1} 2^x $ on $ (-\infty , \infty )$
If $f(x) = \cos (\log x)$, then $f(x)f(y) - \frac{1}{2}[f(x/y) + f(xy)] = $
Statement $-1$ : The equation $x\, log\, x = 2 - x$ is satisfied by at least one value of $x$ lying between $1$ and $2$
Statement $-2$ : The function $f(x) = x\, log\, x$ is an increasing function in $[1, 2]$ and $g (x) = 2 -x$ is a decreasing function in $[ 1 , 2]$ and the graphs represented by these functions intersect at a point in $[ 1 , 2]$
Let $f:(1,3) \rightarrow \mathrm{R}$ be a function defined by
$f(\mathrm{x})=\frac{\mathrm{x}[\mathrm{x}]}{1+\mathrm{x}^{2}},$ where $[\mathrm{x}]$ denotes the greatest
integer $\leq \mathrm{x} .$ Then the range of $f$ is
If $y = 3[x] + 1 = 4[x -1] -10$, then $[x + 2y]$ is equal to (where $[.]$ is $G.I.F.$)
Product of all the solution of the equation ${x^{1 + {{\log }_{10}}x}} = 100000x$ is