#3
A) g(x) is continuous at at.
In this question just by looking at the question, we are able to know that the graph looks very smoothly. Therefore, there should a limit , if g(a)=lim x approaches to a g(x) then g(x) is continuous at a.
B) Function f(w) is continuous at g(a)
Let g(a) is an input fot a function f(w) if f(g(a)) equals to f(w) as limit w approaches to g(a) the f(w) is continuous at g(a)
C) let g(x) is continuous at a and f(w) is continuous at g(a) then f(g(x)) is continuous at a. If g(x) is continuous at a then g(a)=limit g(x) as x approaches to a. Also if f(w) is continuous at g(a), then f(g(a))=f(w) as limit w approaches to g(a). Therefore, the statement f(g(x)) is continuous at a is true since the first and second statement are both true.