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Byju's Answer
Standard XII
Mathematics
Theorems for Continuity
If the functi...
Question
If the function
f
(
x
)
=
x
2
−
(
A
+
2
)
x
+
A
x
−
2
, for
x
≠
2
and
f
(
2
)
=
2
, is continuous at
x
=
2
, then find the value of A.
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Solution
Here, we given that
f
(
x
)
=
x
2
−
(
A
+
2
)
x
+
A
x
−
2
For Remainder,
Let put
x
=
2
in
x
2
−
(
A
+
2
)
x
+
A
.
as we know for continuous function remainder will be zero.
∴
f
(
x
)
=
x
2
−
(
A
+
2
)
x
+
A
f
(
2
)
=
(
2
)
2
−
(
A
+
2
)
(
2
)
+
A
=
4
−
2
A
−
4
+
A
∴
A
=
0
So, function
f
(
x
)
is written as
f
(
x
)
=
x
2
−
(
0
+
2
)
x
+
0
x
−
2
=
x
2
−
2
x
x
−
2
=
x
(
x
−
2
)
(
x
−
2
)
f
(
x
)
=
x
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0
Similar questions
Q.
If the function
f
(
x
)
=
⎧
⎨
⎩
x
2
−
(
A
+
2
)
x
+
2
A
x
−
2
f
o
r
x
≠
2
2
f
o
r
x
=
2
is continuous at
x
=
2
, then-
Q.
If the function
f
(
x
)
=
⎧
⎪
⎨
⎪
⎩
A
x
3
+
x
2
−
(
A
+
2
)
x
+
A
x
−
2
for
x
≠
2
2
for
x
=
2
is continuous at
x
=
2
, then.
Q.
Consider the function
f
(
x
)
=
⎧
⎨
⎩
2
x
−
1
,
0
≤
x
<
2
x
+
a
2
≤
x
≤
4
3
x
+
b
4
<
x
≤
6
(i) Find
f
(
2
−
)
and
f
(
2
+
)
(ii) Find
a
if
f
is continuous at
x
=
2
(iii) Find
b
if
f
is continuous on
[
0
,
6
]
Q.
Let
f
(
x
)
=
21
x
3
+
x
2
−
16
x
+
20
(
x
−
2
)
2
if
x
≠
2
value of f(2) so that is a continuous function.
Q.
If function
f
(
x
)
is continuous in interval
[
−
2
,
2
]
, find the value of
(
a
+
b
)
where
f
(
x
)
=
sin
a
x
x
−
2
,
for
−
2
≤
x
<
0
=
2
x
+
1
,
for
0
≤
x
≤
1
=
2
b
√
x
2
+
3
−
1
,
for
1
<
x
≤
2
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