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If-f-a-function-such-that-f-a-f-b-f-a-b-a-b-find-the-value-of-f-2019-

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Question Number 93464 by i jagooll last updated on 13/May/20
If f a function such that f(a).f(b)−f(a+b)=a+b. find the value of f(2019)
Iffafunctionsuchthatf(a).f(b)−f(a+b)=a+b.findthevalueoff(2019)
Answered by prakash jain last updated on 13/May/20
put b=0 f(a).f(0)−f(a)=a f(a)(f(0)−1)=a a=b=0 (f(0))^2 −f(0)=0 ⇒f(0)=1 or f(0)=0 if f(0)=0⇒f(a)=−a it does not satisfy original equation. ab+(a+b)≠a+b iv f(0)=1 f(a)−f(a)=a not possible Please recheck question. I will check my workings as well.
putb=0f(a).f(0)−f(a)=af(a)(f(0)−1)=aa=b=0(f(0))2−f(0)=0⇒f(0)=1orf(0)=0iff(0)=0⇒f(a)=−aitdoesnotsatisfyoriginalequation.ab+(a+b)≠a+bivf(0)=1f(a)−f(a)=anotpossiblePleaserecheckquestion.Iwillcheckmyworkingsaswell.

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