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
The domain of the function $f(x) = {\sin ^{ - 1}}[{\log _2}(x/2)]$ is
The largest interval lying in $\left( { - \frac{\pi }{2},\frac{\pi }{2}} \right)$ for which the function, $f\left( x \right) = {4^{ - {x^2}}} + {\cos ^{ - 1}}\left( {\frac{x}{2} - 1} \right) + \log \left( {\cos x} \right)$ is defined is
Consider the function $f (x) = x^3 - 8x^2 + 20x -13$
Number of positive integers $x$ for which $f (x)$ is a prime number, is
If $f(x) = \cos (\log x)$, then $f(x)f(y) - \frac{1}{2}[f(x/y) + f(xy)] = $