1f(x+y)=f(x).f(y) implies f(x)=a^kx
Let f(x+y)=f(x).f(y) for all real values of x & y.f(5)=2, \frac{\partial (0)}{\partial x}=3.
then\frac{\partial (5)}{\partial x}=?
a.6 b.3 c.5 d.1
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5 Answers
1correction : take f(x) = ekx . now, if ur ques. is why its taken so,then :
in general terms f ( x ) = ax = elna.x = ekx ( k represents any constant lna )
now, put values of x and y as 0 and 5 respectively, then solve f (5) = 2.
perhaps,u'll get something like k = (ln 2) / 5. now,solve d other two equations to get d answer !
62Let f(x+y)=f(x).f(y) for all real values of x & y.f(5)=2, ∂0/∂x =3.
then ∂5/∂x=?
f(0)=f(0)2, thus, f(0)=1 or 0
f(x)=f(x).f(0)... if f(0)=0, then f(x)=0 for all x.. but f(5)=2. Hence f(0)=1
f(x+y)-f(y)y = (f(x)-1)f(y)y
f(x+y)-f(y)y = (f(x)-1){f(y)-0}y
take Lim y->0
f'(x) = (f(x)-1)f'(0)
f'(5) = {f(5)-1}3 = (2-1)x3 = 3