Let f :R_+ →R such as f(x)=f(x)+f(y) 1) Prove that f is derivable iff f is derivable at x=1. 2) Prove that if so, f(x)=Log_a x) where a is positive value to precise


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Question Number 216532 by sniper237 last updated on 10/Feb/25

$L e t f : R_{+} \to R s u c h a s f (x) = f (x) + f (y)$ $1) P r o v e t h a t f i s d e r i v a b l e i f f$ $f i s d e r i v a b l e a t x = 1 .$ $2) P r o v e t h a t i f s o, f (x) = {L o g}_{a} x)$ $w h e r e a i s p o s i t i v e v a l u e t o p r e c i s e$
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