The function $f(x) =$ ${x^{\frac{1}{{\ln \,x}}}}$

  • A

    is a constant function

  • B

    has a domain $(0, 1) U (e, \infty )$

  • C

    is such that $\mathop {\lim it}\limits_{x \to 1}  f(x) $ exist

  • D

    $(A)$ or $(C)$ both

Similar Questions

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

  • [AIEEE 2007]

Let $f: R \rightarrow R$ be a function defined by $f(x)=(2+3 a) x^2+\left(\frac{a+2}{a-1}\right) x+b, a \neq 1$. If $f(x+y)=f(x)+f(y)+1-\frac{2}{7} x y$, then the value of $28 \sum_{i=1}^3|f(i)|$ is:

  • [JEE MAIN 2025]

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)] = $

  • [IIT 1983]