Let f and g be two real functions; continuous at `x = a` Then `alpha f` and `1/f` is continuous at `x=a` provided `f(a) != 0` and `alpha` is a real number

Let f and g be two real functions; continuous at x=a Then f+g and f-g is continuous at x=a

Let f and g be two real functions; continuous at x=a Then fg and (f)/(g) ia continous at x=a; provided g(a)!=0

Let f and g be two real functions;such that fog is defined.If g is continuous at x=a and f is continuous at g(a); show that fog is continuous at x=a

If f and g are two continuous functions on their common domain D then f.g and (f)/(g) is continuous on D provided g(x) is defined at that point.

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

Let f(x) and g(x) be two equal real function such that f(x)=(x)/(|x|) g(x), x ne 0 If g(0)=g'(0)=0 and f(x) is continuous at x=0, then f'(0) is

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