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Problem
Problem
If
f
(
x
+
1
x
)
=
x
2
+
1
x
2
f\left(x + \frac{1}{x}\right) = x^2 + \frac{1}{x^2}
f
(
x
+
x
1
)
=
x
2
+
x
2
1
,
x
≠
0
x \neq 0
x
=
0
, then
f
(
x
)
=
f(x) =
f
(
x
)
=
(a)
x
2
−
2
x^2 - 2
x
2
−
2
for
∣
x
∣
≥
2
|x| \geq 2
∣
x
∣
≥
2
(b)
2
−
x
2
2 - x^2
2
−
x
2
for
∣
x
∣
≤
2
|x| \leq 2
∣
x
∣
≤
2
(c)
x
2
−
1
x^2 - 1
x
2
−
1
for
∣
x
∣
≥
1
|x| \geq 1
∣
x
∣
≥
1
(d)
x
2
+
1
x^2 + 1
x
2
+
1
for
∣
x
∣
≥
2
|x| \geq 2
∣
x
∣
≥
2
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