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

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

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