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f(x+y)=f(x)+f(y) and f is continuous at 0. Prove that f is continuous at any a.

Question

f(x+y)=f(x)+f(y) and f is continuous at 0. Prove that f is continuous at any a.

check_circleAnswer
Step 1

To show that the continuity at x=0 implies continuity at all x (under the given condition on the function)

Step 2

Recall the definition of continuity of a general function f(x) a a point x

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Step 3

Note that f(...

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Math

Calculus

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