f(x-f(y))=1-x-y

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Solution for f(x-f(y))=1-x-y equation: 


Simplifying
f(x + -1f(y)) = 1 + -1x + -1y

Multiply f * y
f(x + -1fy) = 1 + -1x + -1y

Reorder the terms:
f(-1fy + x) = 1 + -1x + -1y
(-1fy * f + x * f) = 1 + -1x + -1y

Reorder the terms:
(fx + -1f2y) = 1 + -1x + -1y
(fx + -1f2y) = 1 + -1x + -1y

Solving
fx + -1f2y = 1 + -1x + -1y

Solving for variable 'f'.

Reorder the terms:
-1 + fx + -1f2y + x + y = 1 + -1x + -1y + -1 + x + y

Reorder the terms:
-1 + fx + -1f2y + x + y = 1 + -1 + -1x + x + -1y + y

Combine like terms: 1 + -1 = 0
-1 + fx + -1f2y + x + y = 0 + -1x + x + -1y + y
-1 + fx + -1f2y + x + y = -1x + x + -1y + y

Combine like terms: -1x + x = 0
-1 + fx + -1f2y + x + y = 0 + -1y + y
-1 + fx + -1f2y + x + y = -1y + y

Combine like terms: -1y + y = 0
-1 + fx + -1f2y + x + y = 0

The solution to this equation could not be determined.

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