Question

If f, g, h are real functions given by f(x) = x², g(x) = tan x and h(x) = log_e x, then write the value of (hogof) $\left(\sqrt{{\displaystyle \frac{\mathrm{\pi }}{4}}}\right)$.

Answer 1

Given : f(x) = x², g(x) = tan x and h(x) = log_e x.
(hogof) $\left(\sqrt{{\displaystyle \frac{\mathrm{\pi }}{4}}}\right)$ = $h\left(g\left(f\left(\sqrt{\frac{\mathrm{\pi }}{4}}\right)\right)\right)$
$$\begin{gathered} =h\left(g\left({\left(\sqrt{\frac{\mathrm{\pi }}{4}}\right)}^2\right)\right) \\ =h\left(g\left(\frac{\mathrm{\pi }}{4}\right)\right) \\ =h\left(\tan \left(\frac{\mathrm{\pi }}{4}\right)\right) \\ =h\left(1\right) \\ ={\log }_{e}1=0 \end{gathered}$$