If f, g, h are real functions given by f(x) =
Question:

If $f, g, h$ are real functions given by $f(x)=x^{2}, g(x)=\tan x$ and $h(x)=\log _{e} x$, then write the value of (hogof) $\left(\sqrt{\frac{\pi}{4}}\right)$.

Solution:

Given : f(x) = x2g(x) = tan x and h(x) = loge x.

(hogof) $\left(\sqrt{\frac{\pi}{4}}\right)=h\left(g\left(f\left(\sqrt{\frac{\pi}{4}}\right)\right)\right)$

$=h\left(g\left(\left(\sqrt{\frac{\pi}{4}}\right)^{2}\right)\right)$

$=h\left(g\left(\frac{\pi}{4}\right)\right)$

 

$=h\left(\tan \left(\frac{\pi}{4}\right)\right)$

$=h(1)$

 

$=\log _{e} 1=0$

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