What does it mean to divide a function over another? am I asking for the area in common?

Question

say I have these function in the picture here

does f(x)/g(x) in picture A means the red area? and in case the functions didn't cross as in B what does it mean =0 or undefined?

Answer 1

The red area is the integral of $f-g$, the difference between $f$ and $g$.

The function $\frac fg$ has no "nice" geometric interpretation. The function, for example, is not even defined for all values $x$ for which $g(x)=0$.