If the functions and are such that is continuous at and and is discontinuous at but…

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

Problem

If the functions

f: R \to R

and

g: R \to R

are such that

f(x)

is continuous at

x = \alpha

and

f(\alpha) = a

and

g(x)

is discontinuous at

x = a

but

g(f(x))

is continuous at

x = \alpha

, where,

f(x)

and

g(x)

are non-constant functions. (1)

x = \alpha

is an extremum of

f(x)

and

x = a

is an extremum of

g(x)

(2)

x = \alpha

may not be an extremum of

f(x)

and

x = a

is an extremum of

g(x)

(3)

x = \alpha

is an extremum of

f(x)

and

x = a

may not be an extremum of

g(x)

(4) None of the above