Question

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

Answer 1

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.