Question

If f: R $\to$ R ,g : R $\to$ R and h: R $\to$ R are such that f(x) = $x^2$ , g(x) = tan x and h (x) = log x, then the value of (ho (gof)) (x)
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