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Grade: 12

                        

Sir, this is my doubt please clarify, Let f:R->R be a function given by f(x+y) = f(x)+f(y) for all x,y belongs to R such that F91)=a, f(x)= Sir, Kindly give me the solution

4 years ago

Answers : (1)

Faiz
107 Points
							Lim h->0 [ f(x+h) - f(x) ] / h = f`(x)	Lim h->0 [ f(x) + f(h) - f(x) ] / h = f`(x)	As f(x+y) = f(x) + f(y)	Lim h->0 f(h) / h = f`(x)	Transforming into differential eq.	y/x = dy/dx (variable separable)	-> log y = log cx	at x=1 y=a gives c=a	-> log y = log ax	Taking antilog both the sides ans: y = ax
						
4 years ago
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