If f(x) = x^2, g(x) = tan x and h(x) = log x then {h o(g o f)}(√π/4) = ?

Question

Mark (√) against the correct answer in the following:

If f(x) = x², g(x) = tan x and h(x) = log x then \(\{ho(gof)\}(\sqrt{\frac{\pi}{4}})=?\)

A. 0

B. 1

C. \(\frac{1}{x}\)

D. \(\frac{1}{2}log\frac{\pi}{4}\)

Answer 1

Correct Answer is (A) 0

f(x) = x², g(x) = tan x and h(x) = log x

\(\Rightarrow g(f(x))=tan(f(x))=tan(x^2)\)

\(\Rightarrow h(g(f(x)))=log(g(f(x)))=log(tan(x^2))\)

\(\Rightarrow h(g(f(\sqrt{\frac{\pi}{4}})))\)\(=log(tan(\sqrt{\frac{\pi}{4}}))\)\(=log(tan(\frac{\pi}{4}))\)\(=log(1)=0\)