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Show that f(x) = [3/x + 5] is decreasing for all x ∈ R, where x ≠ 0.

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It is given that

f(x) = [3/x + 5]

By differentiating w.r.t. x

f’(x) = 3(-1/x2) = -3/x2 < 0 for all value of R

Therefore, f(x) is decreasing for all x ∈ R, where x ≠ 0.

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