If and are continuous at

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

f

and

g

are continuous at

x=c

, which of the following statements is ALWAYS true? (a)

\displaystyle \frac{f(x)}{g(x)} \text{ is continuous at }x=c\text{ even if }g(c)=0.

(b)

f(x)+g(x)

is continuous at

x=c

. (c)

f(g(x))

is always continuous at

x=c

. (d)

f(x)-g(x)

may fail to be continuous at

x=c