Let f be a real valued function defined on R such that f(x+y)=f(x)+f(y). Suppose there exists at least an element x0∈R such that f is continuous at x. Then prove that f(x)=ax, for some x∈R.
Hints will be appreciated.
Let f be a real valued function defined on R such that f(x+y)=f(x)+f(y). Suppose there exists at least an element x0∈R such that f is continuous at x. Then prove that f(x)=ax, for some x∈R.
Hints will be appreciated.
I have injection f:A→B and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...
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