Maharashtra State BoardHSC Arts 12th Board Exam
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Prove that function f(x) = x-1x, x ∈ R and x ≠ 0 is increasing function - Mathematics and Statistics

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Sum

Prove that function f(x) = `x - 1/x`, x ∈ R and x ≠ 0 is increasing function

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Solution

f(x) = `x - 1/x`, x ∈ R, x ≠ 0

∴ f'(x) = `1 + 1/x^2`

x2 is always positive for x ≠ 0

∴ f′(x) > 0 for all x ∈ R, x ≠ 0

Hence, f(x) is an increasing function for all x ∈ R, x ≠ 0.

Concept: Increasing and Decreasing Functions
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