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Question
Test whether the function is increasing or decreasing.
f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0,
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Solution
f(x) `= "x" - 1/"x", "x" in "R"`
`therefore "f"'("x") = 1 - (- 1/"x"^2) = 1 + 1/"x"^2`
`∵ "x" ne 0,` for all values of x, `"x"^2>0`
`therefore 1/"x"^2 > 0, 1 + 1/"x"^2` is always positive
thus f'(x)>o , for all x ∈ R
Hence f(x) is increasing function.
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