The function $f(x) =$ ${x^{\frac{1}{{\ln \,x}}}}$
is a constant function
has a domain $(0, 1) U (e, \infty )$
is such that $\mathop {\lim it}\limits_{x \to 1} f(x) $ exist
$(A)$ or $(C)$ both
Which of the following is true
The domain of the function $f(x) = {\sin ^{ - 1}}[{\log _2}(x/2)]$ is
If $x \in [0, 1]$, then the number of solution $(s)$ of the equation $2[cos^{-1}x] + 6[sgn(sinx)] = 3$ is (where $[.]$ denotes greatest integer function and sgn $(x)$ denotes signum function of $x$)-
Set of all values of $x$ satisfying
$\frac{{{x^4} - 4{x^3} + 3{x^2}}}{{({x^2} - 4)({x^2} - 7x + 10)}} \ge 0$
If $f(x) = \sin \log x$, then the value of $f(xy) + f\left( {\frac{x}{y}} \right) - 2f(x).\cos \log y$ is equal to