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Question
If f, g, h are real functions given by f(x) = x2, g(x) = tan x and h(x) = loge 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) \[\left( \sqrt{\frac{\pi}{4}} \right)\] = \[h\left( g\left( f\left( \sqrt{\frac{\pi}{4}} \right) \right) \right)\]
\[= h\left( g\left( \left( \sqrt{\frac{\pi}{4}} \right)^2 \right) \right)\]
\[ = h\left( g\left( \frac{\pi}{4} \right) \right)\]
\[ = h\left( \tan \left( \frac{\pi}{4} \right) \right)\]
\[ = h\left( 1 \right)\]
\[ = \log_e 1 = 0\]
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