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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!
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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