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f:R-R....be a differential function satisfying f(y).f(x-y)=f(x) x,y belong to Real nos....f'(5)=q....f(0)/f'(0)=1/p f(5)=???..in terms of p and q.......thanks for help!

f:R-R....be a differential function satisfying  f(y).f(x-y)=f(x)


x,y belong to Real nos....f'(5)=q....f(0)/f'(0)=1/p


f(5)=???..in terms of p and q.......thanks for help!

Grade:11

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear tushara

f(y).f(x-y)=f(x)

replace x by x+y

f(y).f(x)=f(x+y)...........1

put x=y=0

which give f(0)=1

given  f(0)/f'(0)=1/p

   so f'(0)=p

Now

 F'(5) =lim h→0 {f(5+h) -f(5)}/h

           =lim h→0 {f(5)f(h) -f(5)}/h       using the result 1

           =f(5) lim h→0 {f(h) -1}/h

          =f(5) lim h→0 {f(h+0) -f(0)}/h      because f(0) =1

   F'(5)   =f(5)f'(0)

so f(5)=q/p


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Badiuddin


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