If $f(x)=\frac{2 x-3}{3 x-2}$ and $f_n(x)=($ fofofo .......n times) $(x)$, then $f_{32}(x)=$

The domain of the real valued function $f(x)=\sqrt{\cos (\sin x)}+\cos ^{-1}\left(\frac{1+x^2}{2 x}\right)$ is

Let $f: R \rightarrow R$ be a function defined by

$$ f(x)=\left\{\begin{array}{cc} x^2-4 x+3, & \text { if } x<2 \\ x-3, & \text { if } x \geq 2 \end{array}\right. $$

Then, the number of real numbers $x$ for which $f(x)=8$ is

If $f(x)$ and $g(x)$ are two real valued functions such that $f(x)=3 x-2$ and $g(x)=x^2+2$, then $[(g \circ f)+(f \circ g)](x)=$