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Byju's Answer
Standard XII
Mathematics
Modulus Function
If f1x=| | ...
Question
If
f
1
(
x
)
=
|
|
x
|
−
2
|
and
f
n
)
x
)
=
∣
∣
f
n
−
1
(
x
)
−
2
∣
∣
for all
n
≥
2
,
n
∈
N
, then number of solution of the equation
f
2015
(
x
)
=
2
is
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Solution
f
(
x
)
=
|
|
x
|
−
2
|
(
f
n
)
x
=
|
f
m
−
1
(
x
)
−
2
|
f
2015
(
x
)
=
2
No soln=?
=
1
only solution
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Similar questions
Q.
If
f
1
(
x
)
=
x
2
+
10
∀
x
∈
R
and
f
n
(
x
)
=
f
1
(
f
n
−
1
(
x
)
)
∀
n
≥
2
,
n
∈
N
, then evaluate
lim
n
→
∞
f
n
(
x
)
Q.
Define a sequence
⟨
f
0
(
x
)
,
f
1
(
x
)
,
f
2
(
x
)
,
…
⟩
of functions by
f
0
(
x
)
=
1
,
f
1
(
x
)
=
x
,
(
f
n
(
x
)
)
2
−
1
=
f
n
+
1
(
x
)
f
n
−
1
(
x
)
, for
n
≥
1
.
Prove that each
f
n
(
x
)
is a polynomial with integer coefficients.
Q.
Let
f
1
(
x
)
=
e
x
,
f
2
(
x
)
=
e
f
1
(
x
)
,
.
.
.
.
.
f
n
+
1
(
x
)
=
e
f
n
(
x
)
for all
n
≥
1
. The for any fixed
n
,
d
d
x
f
n
(
x
)
is
Q.
If
f
1
(
x
)
=
x
x
−
1
and
f
n
(
x
)
=
f
1
(
f
n
−
1
(
x
)
)
for
n
≥
2
, then the integral value of
x
that satisfies
f
101
(
x
)
=
3
x
is
Q.
If
f
1
(
x
)
=
x
x
−
1
and
f
n
(
x
)
=
f
1
(
f
n
−
1
(
x
)
)
for
n
≥
2
, then the integral value of
x
that satisfies
f
101
(
x
)
=
3
x
is
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