Question

If f:R→R is continuous at a point c∈ R and g:R→R is continuous at f(c)∈R, then the composition g(f(x)) :R→R is continuous at c.

Answer 1

Answer:

The assertion that g(f(x)) is continuous at c is true.

Step-by-step explanation:

$let\\a=\lim_{x\rightarrow c}f(x)$

$\because f(x)$ is continuous at c

$\\\\Similarly\\\\b=\lim_{x\rightarrow f(c)}g(x)$

$\because g(x)$ is continuous at $\ x=f(c)$

$\lim_{x\rightarrow c }g(f(x))=g(f(c))\\\\=g(a)$ which is defined as per given data thus g(f(x)) is continuous at x=c