Mathematics - Functions Question with Solution | TestHub

$f\left(x\right)=\sqrt{x}$

$g\left(x\right)=\tan x$

$h\left(x\right)=\frac{1-x^2}{1+x^2}$
$fog\left(x\right)=\sqrt{\mathrm{t}\mathrm{a}\mathrm{n}x}$
$hofog\left(x\right)=h\left(\sqrt{\mathrm{t}\mathrm{a}\mathrm{n}x}\right)$

$=\frac{1-\tan x}{1+\tan x}=\tan \left(\frac{\pi }{4}-x\right)$
$\varphi \left(x\right)=\mathrm{t}\mathrm{a}\mathrm{n}\left(\frac{\pi }{4}-x\right)$
$\varphi \left(\frac{\pi }{3}\right)=\mathrm{t}\mathrm{a}\mathrm{n}\left(\frac{\pi }{4}-\frac{\pi }{3}\right)$

$=\tan \left(-\frac{\pi }{12}\right)=-\tan \frac{\pi }{12}$

$=\mathrm{t}\mathrm{a}\mathrm{n}\left(\pi -\frac{\pi }{12}\right)=\mathrm{t}\mathrm{a}\mathrm{n}\frac{11\pi }{12}$