what exactly is a function of function?$f(x)=2x$ ,$g=3f$, what exactly is $g$?

The question: a function $f(x)=2x$ with the domain $[1,2]$ the codomain $[2,4]$ the image $[2,4]$ when we take a transformation of this function like $g=3f$, what exactly is this $g$ function is?

My guess:

1. we can think $g$ is the function that takes the domain of $f$ as its own domain, so $g$ is a function $g(x)=6x$ with the domain $[1,2]$ and the codomain $[6,12]$.$x\in[1,2]$


2. we can think $g$ is the composition function $g=h\circ f$ ,here $f(x)=2x$ with the domain $[1,2]$,$h(x)=3x$,with the domain$[2,4]$.

Both of them can make sense, so which one is right?