Answer:
The assertion that g(f(x)) is continuous at c is true.
Step-by-step explanation:
[tex]let\\a=\lim_{x\rightarrow c}f(x)[/tex]
[tex]\because f(x)[/tex] is continuous at c
[tex]\\\\Similarly\\\\b=\lim_{x\rightarrow f(c)}g(x)[/tex]
[tex]\because g(x)[/tex] is continuous at [tex]\ x=f(c)[/tex]
[tex]\lim_{x\rightarrow c }g(f(x))=g(f(c))\\\\=g(a)[/tex] which is defined as per given data thus g(f(x)) is continuous at x=c
