Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
JEE Advanced 2015 Paper 1 Mathematics Q17
Mathematics
Problem
Let
f
(
x
)
=
sin
(
π
6
sin
(
π
2
sin
x
)
)
f(x)=\sin\left(\frac\pi6\sin\left(\frac\pi2\sin x\right)\right)
f
(
x
)
=
sin
(
6
π
sin
(
2
π
sin
x
)
)
for all
x
∈
R
x\in\mathbb R
x
∈
R
and
g
(
x
)
=
π
2
sin
x
g(x)=\frac\pi2\sin x
g
(
x
)
=
2
π
sin
x
for all
x
∈
R
x\in\mathbb R
x
∈
R
. Let
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
denote
f
(
g
(
x
)
)
f(g(x))
f
(
g
(
x
))
and
(
g
∘
f
)
(
x
)
(g\circ f)(x)
(
g
∘
f
)
(
x
)
denote
g
(
f
(
x
)
)
g(f(x))
g
(
f
(
x
))
. Then which of the following is (are) true?
Browse the problem library