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Byju's Answer
Standard XII
Mathematics
f(x) Transforms to f(|x|)
The number of...
Question
The number of solution(s) of
y
=
|
|
x
|
2
−
2
|
x
|
−
2
|
and
y
=
1
is
A
2
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B
3
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C
4
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D
5
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Solution
The correct option is
C
4
Given :
y
=
|
|
x
|
2
−
2
|
x
|
−
2
|
Let us consider curve
y
=
x
2
−
2
x
−
2
⇒
y
=
(
x
−
1
)
2
−
3
The graph of
y
=
x
2
is
Thus, first shifting
y
=
x
2
towards right by
1
unit and then moving the graph down by
3
units, we get graph of
y
=
x
2
−
2
x
−
2
Now, graph of
y
=
|
x
|
2
−
2
|
x
|
−
2
,
is
Now, graph of
y
=
|
|
x
|
2
−
2
|
x
|
−
2
|
,
is
As
y
=
|
|
x
|
2
−
2
|
x
|
−
2
|
and
y
=
1
intersects at four distinct points, hence the number of solutions is
4.
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0
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