Another extrapolation

Algebra Level 4

Let \(f,g: \mathbb{R} \longrightarrow \mathbb{R}\) be two continuous functions.

What do the graphs \(\frac{f(x)}{g(x)}\) and \(f(x)-g(x)\) say about one another?

A: If \(f(x)-g(x) = 0\) then \(\frac{f(x)}{g(x)} = 1\).

B: If \(\frac{f(x)}{g(x)}\) is monotonically increasing on some interval, then \(f(x)-g(x)\) is positive on that interval.

C: None of the above.

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