Let , where and are continuous functions on the open interval . Which of the…

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

Problem

Let

f(x) = \frac{g(x)}{h(x)}

, where

g

and

h

are continuous functions on the open interval

(a, b)

. Which of the following statements is true for

a < x < b

? (1)

f

is continuous at all

x

for which

x \ne 0

(2)

f

is continuous at all

x

for which

g(x) = 0

(3)

f

is continuous at all

x

for which

g(x) \ne 0

(4)

f

is continuous at all

x

for which

h(x) \ne 0