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Finding the Function (Posted on 2023-12-30) Difficulty: 3 of 5
Determine f(x), given that:
f'(x) = f(x+1)

  Submitted by K Sengupta    
Rating: 5.0000 (1 votes)
Solution: (Hide)
f(x)=0 works.
f(x)=e^(x-floor(x)) also works except f' is undefined at the integers.
You can replace floor(x) with ceil(x) or with round(x). The latter shifts the f' problem to the half-integers.
This only works because with f(x)=e^x we have f'(x)=f(x).

For an explanation, refer to the solution submitted by Jer in this location.

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  Subject Author Date
Solutions?Jer2023-12-30 10:54:24
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