Please find f(x)?

Question

If f'(x)=-f(x) and f(1)=1, find f(x). 

 

Answer: e^(1-x)

 

Please show all the work. 

Answer 1

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