Range of the function $f(x) = \sin^2(x^4) + \cos^2(x^4)$ is

Let $f(x) = \frac{1}{2} - \tan \left(\frac{\pi x}{2}\right), -1 < x < 1$ and $g(x) = \sqrt{3 + 4x - 4x^2}$, then the domain of $(f + g)$ is

The set of all real values of $x$ for which $f(x)=\sqrt{\frac{|x|-2}{|x|-3}}$ is a well-defined function is

Let $f(x) = \frac{1}{7 - \sin 5x}$ be a function defined on $R$. Then the range of the function $f(x)$ is equal to:

If $[x]^2-5[x]+6=0$,where $[.]$ denotes the greatest integer function,then

The set of all values of $x$ and the set of all values of $a$ for which the real-valued function $f(x) = \sqrt{\log_a(x - [x])}$ is defined are respectively: