Question

Which conditions guarantee that \[f\circ g\] is continuous at \[c\]?

Options

• \[g\] is continuous at \[c\], and \[f\] is continuous at \[g(c)\].

• \[f\] is continuous at \[c\], and \[g\] is continuous at \[f(c)\].

• \[g(c)=0\], and \[f(c)\neq 0\].

• \[f\] and \[g\] are polynomial functions only.

Answer 1

For a composite function, the inner function \[g\] must be continuous at \[c\]. The outer function \[f\] must be continuous at the resulting value \[g(c)\].