If $f(x) = \frac{x}{{x - 1}} = \frac{1}{y}$, then $f(y) = $

If $f(x)$ satisfies the relation $f\left( {\frac{{5x - 3y}}{2}} \right)\, = \,\frac{{5f(x) - 3f(y)}}{2}\,\forall x,y\in R$ $f(0) = 1, f '(0) = 2$ then period of $sin \ (f(x))$ is

Define a function $f(x)=\frac{16 x^2-96 x+153}{x-3}$ for all real $x \neq 3$. The least positive value of $f(x)$ is

If the graph of non-constant function is symmetric about the point $(3,4)$ , then the value of $\sum\limits_{r = 0}^6 {f(r) + f(3)} $ is equal to

The domain of ${\sin ^{ - 1}}({\log _3}x)$ is

Let $f(\theta ) = \sin \theta (\sin \theta + \sin 3\theta )$, then $f(\theta )$