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Question
If f is a real function satisfying \[f\left( x + \frac{1}{x} \right) = x^2 + \frac{1}{x^2}\]
for all x ∈ R − {0}, then write the expression for f(x).
Solution
Given:
\[f\left( x + \frac{1}{x} \right) = x^2 + \frac{1}{x^2}\]
\[= x^2 + \frac{1}{x^2} + 2 - 2\]
f (x) = x2 - 2 , where | x | ≥ 2.
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