Mathematics

Mathematics

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. a.

x = \alpha

is an extremum of

f(x)

and

x = a

is an extremum of

g(x)

b.

x = \alpha

may not be an extremum of

f(x)

and

x = a

is an extremum of

g(x)

c.

x = \alpha

is an extremum of

f(x)

and

x = a

may not be an extremum of

g(x)

d. None of the above

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