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Byju's Answer
Standard XII
Mathematics
Definition of Functions
The three sol...
Question
The three solutions of the equation
f
(
x
)
=
0
are
−
4
,
8
,
and
11.
Therefore, the three solutions of the equation
f
(
2
x
)
=
0
are
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Solution
If
f
(
x
)
=
0
at
x
=
−
4
,
8
and
11
then
f
(
2
x
)
=
0
for
2
x
=
−
4
,
2
x
=
8
a
n
d
2
x
=
11
Solve the above equations to find
x
=
−
2
,
x
=
4
and
x
=
11
2
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Similar questions
Q.
Let
f
(
x
)
=
l
n
m
x
(
m
>
0
)
and
g
(
x
)
=
p
x
. Then t
he equation
|
f
(
x
)
|
=
g
(
x
)
has exactly three solutions for
Q.
The three roots of the equation
f
(
x
)
=
0
are
x
=
−
2
,
0
,
3
. What are the three value of
x
for which
f
(
x
−
3
)
=
0
?
Q.
If
y
=
f
1
(
x
)
and
y
=
f
2
(
x
)
are two solutions of the equation
y
d
x
+
d
y
=
−
e
x
y
2
d
y
, where
f
1
(
0
)
=
1
and
f
2
(
0
)
=
−
1
.
The number of solutions of the equation
f
1
(
x
)
.
f
2
(
x
)
+
x
2
=
0
is/are
Q.
How many solutions of the equation 15x - 14y + 11 = 0 are possible?
Q.
Suppose equation
f
(
x
)
−
g
(
x
)
=
0
or
f
(
x
)
=
g
(
x
)
=
y
say, then draw the graphs of
y
=
f
(
x
)
and
y
=
g
(
x
)
. If graphs of
y
=
f
(
x
)
and
y
=
g
(
x
)
cuts at one, two, three, no points, then number of solutions are one, two, three,zero respectively. On the basis of above information, answer the following question.
Total number of solutions of
cos
2
x
=
|
sin
x
|
, where
x
∈
(
−
π
2
,
π
)
is:
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