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Functions question

2015 · Shift 1 · Q40

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PYQ Library
JEE Advanced
Mathematics
Functions
2015 · Shift 1 · Q40

Functions question

2015 · Shift 1 · Q40

JEE AdvancedMathematicsFunctionsMultiple correct+4 / −2

Let

f(x) = \sin \left( {{\pi \over 6}\sin \left( {{\pi \over 2}\sin x} \right)} \right)

for all

x \in R

and g(x) =

{{\pi \over 2}\sin x}

for all x

\in

R. Let

(f \circ g)(x)

denote f(g(x)) and

(g \circ f)(x)

denote g(f(x)). Then which of the following is/are true?

A
Range of f is $\left[ { - {1 \over 2},{1 \over 2}} \right]$ .
B
Range of f $\circ$ g is $\left[ { - {1 \over 2},{1 \over 2}} \right]$ .
C
$\mathop {\lim }\limits_{x \to 0} {{f(x)} \over {g(x)}} = {\pi \over 6}$ .
D
There is an x $\in$ R such that (g $\circ$ f)(x) = 1.

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