1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
How to Find the Inverse of a Function
If f:R→ R i...
Question
If
f
:
R
→
R
is given by
f
(
x
)
=
x
3
, write
f
−
1
(
1
)
.
Open in App
Solution
f
:
R
→
R
is given by
f
(
x
)
=
x
3
.
Let
f
−
1
(
1
)
=
x
---- ( 1 )
⇒
f
(
x
)
=
1
⇒
x
3
=
1
...................
[ Given ]
⇒
x
3
−
1
=
0
⇒
(
x
−
1
)
(
x
2
+
x
+
1
)
=
0
...................
[ Since,
a
3
−
b
3
=
(
a
+
b
)
(
a
2
+
a
b
+
b
2
)
]
Value of
x
of
x
2
+
x
+
1
will be complex number.
As
x
∈
R
, then
x
2
+
x
+
1
=
0
is not possible.
⇒
x
−
1
=
0
⇒
x
=
1
From ( 1 ),
⇒
f
−
1
(
1
)
=
{
1
}
Suggest Corrections
0
Similar questions
Q.
If f : R → R is given by f(x) = x
3
, write f
−1
(1).
Q.
If f : R → R be defined by f(x) = x
4
, write f
−1
(1).
Q.
If f : R → R is defined by f(x) = x
2
, write f
−1
(25).
Q.
If
f
: R → R be given by
, then
f
o
f
(
x
) is
(A)
(B)
x
3
(C)
x
(D) (3 −
x
3
)