If the functions \( f: R \rightarrow R \) and \( g: R \rightarrow R \) are such that
P \( f(x) \) is continuous at \( x=\alpha \) and \( f(\alpha)=a \) and \( g(x) \) is
W 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 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
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