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Problem
Problem
Let
f
:
N
→
N
f: N \rightarrow N
f
:
N
→
N
, where
f
(
x
)
=
x
+
(
−
1
)
x
−
1
f(x) = x + (-1)^{x-1}
f
(
x
)
=
x
+
(
−
1
)
x
−
1
, then the inverse of
f
f
f
is. (a)
f
−
1
(
x
)
=
x
+
(
−
1
)
x
−
1
,
x
∈
N
f^{-1}(x) = x + (-1)^{x-1}, x \in N
f
−
1
(
x
)
=
x
+
(
−
1
)
x
−
1
,
x
∈
N
(b)
f
−
1
(
x
)
=
3
x
+
(
−
1
)
x
−
1
,
x
∈
N
f^{-1}(x) = 3x + (-1)^{x-1}, x \in N
f
−
1
(
x
)
=
3
x
+
(
−
1
)
x
−
1
,
x
∈
N
(c)
f
−
1
(
x
)
=
x
,
x
∈
N
f^{-1}(x) = x, x \in N
f
−
1
(
x
)
=
x
,
x
∈
N
(d)
f
−
1
(
x
)
=
(
−
1
)
x
−
1
,
x
∈
N
f^{-1}(x) = (-1)^{x-1}, x \in N
f
−
1
(
x
)
=
(
−
1
)
x
−
1
,
x
∈
N
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