FunctionHard
Question
If y = f(x) satisfies the condition f(x + 1/x) = x2 + 1/x2 (x ≠ 0), then f(x) is equal to
Options
A.- x2 + 2
B.- x2 - 2
C.x2 - 2, x ∈ R - {0}
D.x2 - 2, |x| ∈ [2, ∞)
Solution
f
= x2 + 
x +
= t |t| ≥ 2
∴ f(t) = t2 - 2, |t| ≥ 2
= x2 + x +
= t |t| ≥ 2∴ f(t) = t2 - 2, |t| ≥ 2
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