- #1

the problem is

prove that if f(a+b)=f(a)f(b) for all a and b ,then f is cntiniuous at every real number.here there is given information that is the domain of f is the set of all real number and f is continuous at 0.

I tried to approache this problem like this

since f is continuous at 0, f(0) must defined and it must be equal to the value of limf(x) =f(0)

x-->0

and a and b are real numbers then limf(a+b)=limf(a).limf(b)

x--->0 x-->0 x-->0

=f(a).f(b) (since f(a) and f(b) are constnt fu.)

this implies f is continuous at every real number.

am i write? i want to be sure so please help