Doubt from Continuity and Differentiability

Please tell about option B.

bro h(f(x)) will tend to I1 only when f(x)(when x tends to a- ) and f(x) (when x tends to a+) both approch k from negative side coz you now if one of them doesn’t then LHL will not be equal to RHL
(as both limits are different)
for h(x) thus the limit won’t exist…
now according to various cases arising for I1 and K u may get a maxima or minima( terms and conditions apply)
but k would be a extremum for f(x)

thanks bro.But I didn’t understood it.I mean why h (f (x)) need to be tend to I1? Can’t it tend to I2?
Please explain… @mihir

because they have mentioned that lim(x->i1) g(x ) exists but they haven’t mentioned about g(i2)…so

but is it necessary that it’s only I1 at which limit of g (x) exists? Can’t it maybe be some other point ?

bro it could if it was mentioned that g(x) is a continuous function.but it since it’s not mentioned one cannot say…