If $$f:R \to R,\,g:R \to R$$     and $$h:R \to R$$   are such that $$f\left( x \right) = {x^2},\,g\left( x \right) = \tan \,x$$     and $$h\left( x \right) = \log \,x,$$   then the value of $$\left( {ho\left( {gof} \right)} \right)\left( x \right)$$   if $$x = \sqrt {\frac{\pi }{4}} $$  will be :

Solution :
$$\eqalign{ & \left( {ho\left( {gof} \right)} \right)\left( x \right) = h\left\{ {g\left\{ {f\left( x \right)} \right\}} \right\} \cr & = h\left\{ {\tan \,{x^2}} \right\} \cr & = \log \left\{ {\tan \,{x^2}} \right\} \cr & \therefore {\text{ At }}x = \sqrt {\frac{\pi }{4}} \cr & \Rightarrow \left( {ho\left( {gof} \right)} \right)\left( x \right) = \log \,\tan \,\frac{\pi }{4} \cr & \Rightarrow \left( {ho\left( {gof} \right)} \right)\left( x \right) = \log \,1 = 0 \cr} $$