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) = x2, g(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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