If 2 f ( x )= f ^ (x) and f (0)=3 , then the value of f (2) is

Step-by-step solution

We have f^ (x)=2 f(x) array l f ^ ( x ) f ( x ) d x = 2 ~d x | f ( x )|=2 x + c array Now f(0)=3 array l | 3|=0+c c= 3 |f(x)|=2 x+ 3 array When x=2 , aligned & | f (2)|=2(2)+ 3=4+ 3 & f (2)= e ^ 4+ 3 = e ⁴ e ^ 3 =3 e ⁴ aligned