Q.9 Test whether the function f(x) = x - 1/x,\ x in R,\ x ≠ 0 is increasing or decreasing.

Answer: f is increasing (for all x ≠ 0 ). f'(x) = 1 + 1/x² . For every x ≠ 0 , x² gt 0 , so 1/x² gt 0 and f'(x) = 1 + 1/x² gt 0 . Hence f is an increasing function (on each of the intervals x lt 0 and x gt 0 ).

Test whether the function \(f(x) = x - \frac{1}{x},\ x \in R,\ x \ne 0\) is increasing or decreasing.

Q.9 Test whether the function \(f(x) = x - \frac{1}{x},\ x \in R,\ x \ne 0\) is increasing or decreasing.

Doubtly Asked 28 Oct 2026 Board exam · June 2026 hsc 12th Save WhatsApp Report

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Answer: f is increasing (for all \(x \ne 0\)).

\(f'(x) = 1 + \frac{1}{x^2}\).

For every \(x \ne 0\), \(x^2 \gt 0\), so \(\frac{1}{x^2} \gt 0\) and \(f'(x) = 1 + \frac{1}{x^2} \gt 0\). Hence \(f\) is an increasing function (on each of the intervals \(x \lt 0\) and \(x \gt 0\)).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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Test whether the function \(f(x) = x - \frac{1}{x},\ x \in R,\ x \ne 0\) is increasing or decreasing.

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