Let $f$ be a real valued function defined by

$f(x) = sin^{-1} \left( {\frac{{\,\,1 - \,\,\left| x \right|}}{3}} \right) + cos^{-1}\left( {\frac{{\left| x \right|\,\, - \,\,3}}{5}} \right)$ .

Then domain of $f(x)$ is given by :

Suppose that a function $f: R \rightarrow R$ satisfies $f(x+y)=f(x) f(y)$ for all $x, y \in R$ and $f(1)=3 .$ If $\sum \limits_{i=1}^{n} f(i)=363,$ then $n$ is equal to

Consider a function $f : N \rightarrow R$, satisfying $f(1)+2 f(2)+3 f(3)+\ldots+x f(x)=x(x+1) f(x) ; x \geq 2$ with $f(1)=1$. Then $\frac{1}{f(2022)}+\frac{1}{f(2028)}$ is equal to

Let $f(x) = {(x + 1)^2} - 1,\;\;(x \ge - 1)$. Then the set $S = \{ x:f(x) = {f^{ - 1}}(x)\} $ is

Which of the following is correct

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