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p { margin-bottom: 0.25cm; line-height: 120%; } A function f : R --> R ,satifies the equation f ( x + y )= f(x)(y) for all x,y є R and f(x) is not equal to 0 for any x in R.If x be differentiable at x=0 and f’(0) =2,show that for all x є R, f’(x)=2f(x)

p { margin-bottom: 0.25cm; line-height: 120%; }

A function f:R-->R,satifies the equation f(x+y)=f(x)(y) for all x,yєR and f(x) is not equal to 0 for any x in R.If x be differentiable at x=0 and f’(0)=2,show that for all xєR,

f’(x)=2f(x)

Grade:11

1 Answers

Anish Singhal
askIITians Faculty 1194 Points
2 years ago
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