# 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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