Let f:R→Rf:R→R a derivable function but not zero, such that f′(0)=2 and f(x+y)=f(x)⋅ f(y) for all x and y belongs R. Find f(x)

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Himanshu · Answer

Differentiate w.r.t x both sides then put x=0 & y=x,then solve after solving you get ln(f(x))=-2x+c;c is constant of integration.

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Let f:R→Rf:R→R a derivable function but not zero, such that f′(0)=2 and f(x+y)=f(x)⋅ f(y) for all x and y belongs R. Find f(x)

Let f:R→Rf:R→R a derivable function but not zero, such that f′(0)=2 and f(x+y)=f(x)⋅ f(y) for all x and y belongs R. Find f(x)

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Let f:R→Rf:R→R a derivable function but not zero, such that f′(0)=2 and f(x+y)=f(x)⋅ f(y) for all x and y belongs R. Find f(x)

Let f:R→Rf:R→R a derivable function but not zero, such that f′(0)=2 and f(x+y)=f(x)⋅ f(y) for all x and y belongs R. Find f(x)

1 Answers

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