Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
1
+
x
f(x) = \frac{x}{1+x}
f
(
x
)
=
1
+
x
x
and
g
(
x
)
=
r
x
1
−
x
g(x) = \frac{rx}{1-x}
g
(
x
)
=
1
−
x
r
x
. Let
S
S
S
be the set of all real numbers
r
r
r
, such that
f
(
g
(
x
)
)
=
g
(
f
(
x
)
)
f(g(x)) = g(f(x))
f
(
g
(
x
))
=
g
(
f
(
x
))
for infinitely many real numbers
x
x
x
. The number of elements in set
S
S
S
is a. 1 b. 2 c. 3 d. 5
Browse the problem library