Show that f is continuous at every point in R

[acacia89]

Suppose a function f : R → R satisfy f(x + y) = f(x) + f(y) and f is continuous
at x = 0: Show that f is continuous at every point in R.

(Hint: Using the fact that
lim f(x) = l implies
x→x0
limf(x0+h)= l
h→0 )

 

[LCKurtz]

Suppose a function f : R → R satisfy f(x + y) = f(x) + f(y) and f is continuous
at x = 0: Show that f is continuous at every point in R.

(Hint: Using the fact that
lim f(x) = l implies
x→x0
limf(x0+h)= l
h→0 )

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