If `f(x)= alpha x+beta` and `f(0)=f^(')(0)=1` then `f(2)` =

If f(x)=alpha x+beta and f(0)=f^(1)(0)=1 then f(2) =

If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f^(')(x)^(2)=0 AA x in R and f(0)=1=f^(')(0) . Then find f(x) .

If alpha,beta!=0 , and f(n)""=alpha^n+beta^n and |3 1+f(1)1+f(2)1+f(1)1+f(2)1+f(3)1+f(2)1+f(3)1+f(4)|=K(1-alpha)^2(1-beta)^2(alpha-beta)^2 , then K is equal to (1) alphabeta (2) 1/(alphabeta) (3) 1 (4) -1

If f'(x)=f(x) and f(0)=1 then lim_(x rarr0)(f(x)-1)/(x)=

Let f:R rarr R be defined by f(x)=2+alpha x,alpha!=0 , If f(x)=f^(-1)(x) , for all x in R , then alpha equals

If f'(x)>0,f(x)>0AA x in(0,1) and f(0)=0,f(1)=1, then prove that 'f(x)f^(^^)-1(x)

Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1) =5 alpha'(2) =7 then 2nd the vlaue of beta'(1)-10

Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists and f'(0) = - sin alpha , then f{f'(0)} is