Functions Test ...

Let $f(x)=\cos^{-1}(3x-1)$. Then, dom $(f)=?$

Let $f(x)=\sqrt{\cos x}$. Then, dom $(f)=?$

Let $f(x)=log(1-x)+\sqrt{x^2-1}$. Then, dom$(f)=?$

Which of the following is not true about $h_2(x)$

If $f(x)=\dfrac{2}{x-3}, g(x)=\dfrac{x-3}{x+4}$ and $h(x)=-\dfrac{2(2 x+1)}{x^{2}+x-12}$ then $\lim _{x \rightarrow 3}[f(x)+g(x)+h(x)]$ is

For  a real number y, let [y] denotes the greatest integer less than or equal to y. Then the function
$f(x)= \dfrac{tan(\pi \left[ x-\pi  \right ])}{1+[x]^2}$ is

The number of roots of the equation g(x) = 1 is

The domain of the function $f(x) = \sqrt{\ln_{(|x| - 1)} \left (x^{2} + 4x +4 \right )}$ is 

If $f : X \rightarrow Y$, where  $X$ and $Y$ are sets containing natural numbers, $f(x) = \frac{x + 5} {x + 2}$ then the number of elements in the domain and range of $$f(x) are respectively

The domain of definition of the function $f(x)$ given by the equation $2^x + 2^y = 2$ is                                                                  (IIT-JEE, 2000)