if f(xy) = f(x) f(y) for all x and y and if f(x) is continuous at x = 1, then show that it is continuous for all x except 0

if f(x+y)=f(x)+ f(y) for all x and y and if f(x) is continuous at x=0, show that f(x) is continuous everywhere.

Prove that f (x) =|x| is continuous at x =0

If f(x)=(sinx)^(sinx) for all 0ltxltpi , find f'(x) .

Show that f (x) = f(x) = {(x,sinfrac(1)(x)),(0,x=0):} is continuous at x = 0

Prove that f(x) = sin x and f(x) = cos x are continuous.

Show that f (x) = |x| is continuous at x= 0 but f'(0) does not exist

If f(x)=(x) and g(x)=(5x-2) Find f0g and g0f

If the function f(x)={{:((sin x)/(x) + cos x", if " x ne 0 ), (k", if " x =0 ):} is continuous at x=0, then find the value of k.

Prove that the constant function f (x)= k, where k is a constant, is continuous