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Question
Mathematics
For a suitably chosen real constant a, let a function, f: R - - a arrow R be defined by f( x )=( a - x / a + x ) Further suppose that for any real number x ≠-a and f(x) ≠-a,(f o f)(x)=x Then f(-(1/2)) is equal to :
Q. For a suitably chosen real constant a, let a function,
f
:
R
−
{
−
a
}
→
R
be defined by
f
(
x
)
=
a
+
x
a
−
x
Further suppose that for any real number
x
=
−
a
and
f
(
x
)
=
−
a
,
(
f
o
f
)
(
x
)
=
x
Then
f
(
−
2
1
)
is equal to :
3650
177
JEE Main
JEE Main 2020
Relations and Functions - Part 2
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A
3
1
14%
B
3
64%
C
−
3
11%
D
−
3
1
10%
Solution:
f
(
x
)
=
a
+
x
a
−
x
x
∈
R
−
{
−
a
}
→
R
f
(
f
(
x
))
=
a
+
f
(
x
)
a
−
f
(
x
)
=
a
+
(
a
+
x
a
−
x
)
a
−
(
a
+
x
a
−
x
)
f
(
f
(
x
))
=
(
a
2
+
a
)
+
x
(
a
−
1
)
(
a
2
−
a
)
+
x
(
a
+
1
)
=
x
⇒
(
a
2
−
a
)
+
x
(
a
+
1
)
=
(
a
2
+
a
)
x
+
x
2
(
a
−
1
)
⇒
a
(
a
−
1
)
+
x
(
1
−
a
2
)
−
x
2
(
a
−
1
)
=
0
⇒
a
=
1
f
(
x
)
=
1
+
x
1
−
x
f
(
2
−
1
)
=
1
−
2
1
1
+
2
1
=
3