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Byju's Answer
Standard XII
Mathematics
How to Find the Inverse of a Function
Let C denot...
Question
Let
C
denote the set of all complex numbers. A function
f
:
C
→
C
is defined by
f
(
x
)
=
x
3
. Write
f
−
1
(
1
)
.
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Solution
Let
f
−
1
(
1
)
=
x
---- ( 1 )
⇒
f
(
x
)
=
1
⇒
x
3
=
1
...................
[ Given ]
⇒
(
x
−
1
)
(
x
2
+
x
+
1
)
=
0
[ Since,
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
]
After solving
x
2
+
x
+
1
=
0
,
we get
x
=
1
±
√
3
i
2
Let,
w
=
1
±
√
3
i
2
⇒
(
x
−
1
)
(
x
−
w
)
(
x
−
w
2
)
=
0
⇒
x
=
1
,
w
,
w
2
[ As
x
∈
C
]
From ( 1 ),
⇒
f
−
1
(
1
)
=
{
1
,
w
,
w
2
}
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