Find the Value of Composite Function
If \(f,\ g,\ h\) are real functions given by
\[ f(x)=x^2, \qquad g(x)=\tan x, \qquad h(x)=\log_e x \]
then write the value of
\[ (h\circ g\circ f)\left(\frac{\sqrt{\pi}}{4}\right) \]
First,
\[ f\left(\frac{\sqrt{\pi}}{4}\right) = \left(\frac{\sqrt{\pi}}{4}\right)^2 \]
\[ =\frac{\pi}{16} \]
Now,
\[ g\left(\frac{\pi}{16}\right) = \tan\frac{\pi}{16} \]
Therefore,
\[ h\left(\tan\frac{\pi}{16}\right) = \log_e\left(\tan\frac{\pi}{16}\right) \]
Hence,
\[ \boxed{ (h\circ g\circ f)\left(\frac{\sqrt{\pi}}{4}\right) = \log_e\left(\tan\frac{\pi}{16}\right) } \]