what do i do when there is a square root in a composite number and how do i determine the domain

Question

determine composite functions and their domains:

f(x) = Squareroot x -1

g(x) = 2x+5

what is (gof)(x)=

what is the domain of f:

what is the domain of g:

what is the domain of (gof)(x)=

Answer 1

f(x)=√(x-1), g(x)=2x+5, (g∘f)(x)=g(f(x))=2f(x)+5=2√(x-1)+5.

Domain of f is x≥1. Can be written x∈[1,∞).

Domain of g is any x. Can be written x∈(-∞,∞).

Domain of (g∘f)(x) is x(g∘f)(x)≥1 (as f)