No, it means that the image of m under the function f is also the image of m under the function g.

Basically, what's in brackets f(...) or g(...) will be the element that will have the image. f(...) and g(...) represent the images.

Almost !

It's not x, it's m, since it is said that $\displaystyle f(m)=g(m)$

$\displaystyle f(m)$ is rewritten : $\displaystyle \frac{2m+1}{3}$ and g(m)...

It's not quite the same as your question of several days ago, because here, you're dealing with two functions. And there is no real question to ask