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)\[\left( \sqrt{\frac{\pi}{4}} \right)\] .

 

Answer 1

Given : f(x) = x², g(x) = tan x and h(x) = log_e x.
(hogof) \[\left( \sqrt{\frac{\pi}{4}} \right)\] =  \[h\left( g\left( f\left( \sqrt{\frac{\pi}{4}} \right) \right) \right)\]

\[= h\left( g\left( \left( \sqrt{\frac{\pi}{4}} \right)^2 \right) \right)\]
\[ = h\left( g\left( \frac{\pi}{4} \right) \right)\]
\[ = h\left( \tan \left( \frac{\pi}{4} \right) \right)\]
\[ = h\left( 1 \right)\]
\[ = \log_e 1 = 0\]