If the functions `f : R -> R` and `g : R -> 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` extremum of `f(x)` and `x=alpha` is an extremum `g(x)` (b) `x=alpha` may not be extremum `f(x)` and `x=alpha` is an extermum of `g(x)` (c) `x=alpha` is an extremum of `f(x)`and `x=alpha` may not be an extremum `g(x)` (d) not of the above

Options

A. `x = alpha` is a 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

Answer

C