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Please find f(x)?

If f'(x)=-f(x) and f(1)=1, find f(x). 
 
Answer: e^(1-x)
 
Please show all the work. 
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1 Answer

df/dx=-f, df/f=-dx, integrating both sides ln(f)=-x +c, at x=1 f(1)=1 so c=1, ln(f)=-x+1, and f(x)=e(1-x)
 
Jim

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