Mark (√) against the correct answer in the following:
Question:

Mark (√) against the correct answer in the following:

If $f(x)=x^{2}, g(x)=\tan x$ and $h(x)=\log x$ then $\{h \circ(g \circ f)\}\left(\sqrt{\frac{\pi}{4}}\right)=?$

A. 0

B. 1

C. $\frac{1}{\mathrm{x}}$

D. $\frac{1}{2} \log \frac{\pi}{4}$

 

Solution:

$f(x)=x^{2}, g(x)=\tan x$ and $h(x)=\log x$

$\Rightarrow \mathrm{g}(\mathrm{f}(\mathrm{x}))=\tan (\mathrm{f}(\mathrm{x}))=\tan \left(\mathrm{x}^{2}\right)$

$\Rightarrow \mathrm{h}(\mathrm{g}(\mathrm{f}(\mathrm{x})))=\log (\mathrm{g}(\mathrm{f}(\mathrm{x})))=\log \left(\tan \left(\mathrm{x}^{2}\right)\right)$

$\Rightarrow \mathrm{h}\left(\mathrm{g}\left(\mathrm{f}\left(\sqrt{\frac{\pi}{4}}\right)\right)\right)=\log \left(\tan \left(\sqrt{\frac{\pi^{2}}{4}}\right)\right)=\log \left(\tan \left(\frac{\pi}{4}\right)\right)=\log (1)=0$

 

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