We have the expression:
[tex](fog)(x)=\sqrt[]{2x}+19[/tex]
So:
[tex]g(x)=2x[/tex][tex]f(x)=\sqrt[]{x}+19[/tex]
***
Since we want to get the function g composed in the function f, and the result of this is:
[tex](fog)(x)=\sqrt[]{2x}+19[/tex]
When we replace g in f, we have to get as answer the previous expression. And by looking at it the only place where we will be able to replace values is where the variable x is located. The function f will have the "skeleton" or shape of the overall function and g will be injected in it.
From this, we can have that f might be x + 19 and g might be sqrt(2x), but the only options that are given such that when we replace g in x of f, are f = sqrt(x) + 19 and g = 2x.
