How to solve Q24 Also how is f(0) = 1 Hence. at -
,qrt6)
So /(x) — 51 not differentiablo at x 5
Q. 24ßunction f : R • R satisfies the equation + y) f f (Y)
y e R, f(x) O. Suppose that the function is differentiable
and f'(O) = 2, then prove that f' (x) = 2 f (x).
SOL —'R satisfies the equation '(r y). fly). V & y e R O
Let '(x)js differentiable O and t' (O) 2,
(O. h) rt0)
2 n 11m
h
2 'im ¯
sol.
SOL
lim
h
z 2t(x)
lusngsq

The solution is correct f(0)!= 1 actually in the step where it seems it is written f(0)=1 there f(0) is being taken as common As f(0).f(h)+f(0) = f(0) ( f(h) + 1 )