Let f(x)=\sin(\pi/6sin(\pi/2sin x)) for all" x ∊\mathbb{R}\text{and}g(x)=\pi/2\text{for all} x ∊\mathbb{R}.Let (f o g)(x) denote f(g(x)) and (g o f)(x) denote g(f(x)).Then which of the following is (are) true ? [JEE Adv 2015 P1]

Range of f \text{is} [-1/2,1/2]

{lim}_{x\to0}\frac{f(x)}{g(x)}=\pi/6

There is an x∊\mathbb{R} such that (g o f)(x)=1

Functions

Section: Mathematics

Question : 18 of 30

Marks: +1, -0

Let f(x)=sin(

sin(

sinx)) for all" x∊ℝ‌and‌g(x)=

for all‌x∊ℝ‌.Let (f o g)(x) denote f(g(x)) and (g o f)(x) denote g(f(x)).Then which of the following is (are) true ?

[JEE Adv 2015 P1]

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