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