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KEAM 2016 Math Paper
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© examsnet.com
Question : 2
Total: 120
The domain of the function
f
(
x
)
=
{
(
x
2
−
9
)
(
x
−
3
)
if
x
≠
3
6
if
x
=
3
}
is
(
0
,
3
)
(
−
∞
,
3
)
(
−
∞
,
∞
)
(
3
,
∞
)
(
−
3
,
3
)
Validate
Solution:
Given,
f
(
x
)
=
{
x
2
−
9
x
−
3
x
≠
3
6
x
=
3.
at
x
=
3
LHL
=
lim
x
→
3
−
x
2
−
9
x
−
3
=
lim
x
→
3
−
(
x
+
3
)
=
lim
h
→
0
(
3
−
h
+
3
)
=
6
RHL
=
lim
x
→
3
+
x
2
−
9
x
−
3
=
lim
x
→
3
+
(
x
+
3
)
=
lim
h
→
0
(
3
+
h
+
3
)
=
6
⇒
f
(
3
)
=
6
∴
L
H
L
=
R
H
L
=
f
(
3
)
Hence,
f
(
x
)
is continuous at
x
=
3
∴ Domain of
f
(
x
)
=
(
−
∞
,
∞
)
© examsnet.com
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