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Suppose f(x) is a function such that f(x) + x = f(y) + y for all real numbers x and y.  If f(-1) = 5 then compute f(-1001).

 Feb 6, 2021
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As follows:

 

\(f(-1) - 1 =f(-1001) - 1001\\ 5 - 1= f(-1001)-1001\\f(-1001)=1005\)

 Feb 6, 2021

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