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Mathematics, 04.10.2021 19:30 quetzaliescalona

Let f be a real-valued function defined on [0,∞), with the properties: f is continuous on [0, ∞), f(0) = 0

f ..1 exists on (0, ∞), and f ..1

0 is monotone increasing on (0,∞).

Let g be the function given by: g(x) = f(x)

for x ∈ (0, ∞).

How do I prove that g is monotone increasing on (0,∞)?

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