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Show that f(x) = [x – 1/x] is increasing for all x ∈ R, where x ≠ 0. |
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Answer» It is given that f(x) = [x – 1/x] By differentiating w.r.t. x f’(x) = 1 + 1/x2 On further calculation f’(x) = (x2 + 1)/x2 Here f’(x) ≥ 0 for all x ≠ 0 Therefore, f(x) is increasing function for all x ∈ R, where x ≠ 0. |
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