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Byju's Answer
Standard XI
Mathematics
Real Valued Functions
The number of...
Question
The number of values of
x
satisfying the equation
1
+
x
=
sgn
(
x
)
is
(where
sgn
(
x
)
denotes the signum function)
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Solution
sgn
(
x
)
=
⎧
⎨
⎩
−
1
,
x
<
0
0
,
x
=
0
1
,
x
>
0
Now,
If
x
>
0
,
1
+
x
=
1
⇒
x
=
0
(rejected)
If
x
=
0
,
1
+
x
=
0
⇒
x
=
−
1
(rejected)
If
x
<
0
,
1
+
x
=
−
1
⇒
x
=
−
2
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