Question

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

• A. 1
• B. -1
• C. $\pi$

Answer 1

$\left(ho\right(gof\left)\right)\left(x\right)=h\left\{g\right\{f\left(x\right)\left\}\right\}$
$=h\left\{tan{x}^2\right\}=log\left\{tan{x}^2\right\}$
$\therefore Atx=\sqrt{\frac{\pi }{4}}\Rightarrow \left(ho\right(gof\left)\right)\left(x\right)=logtan\frac{\pi }{4}$
= log 1 = 0