Suppose is continuous at and is continuous at

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

Problem

Suppose

g

is continuous at

x=2

and

f

is continuous at

g(2)=5

. Let

h(x)=f\bigl(g(x)\bigr)

. Which of the following statements is true concerning the continuity of

h

x=2

? (a)

h

is continuous at

x=2

only if

f

is differentiable at 5. (b) There is not enough information to determine whether

h

is continuous at

x=2

. (c)

h

is continuous at

x=2

. (d)

h

is continuous at

x=2

only if

f

is continuous at 2.