Given f (x-1 / x) = x2 + 1 / X2, the expression of function f (x) is

Let t = X-1 / X,
Because x ≠ 0, t ∈ R,
And from T ^ 2 = (x-1 / x) ^ 2 = x ^ 2 + 1 / x ^ 2-2, x ^ 2 + 1 / x ^ 2 = T ^ 2 + 2,
So f (T) = T ^ 2 + 2,
Therefore, the expression of function f (x) is f (x) = x ^ 2 + 2 (x ∈ R)

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