k(x)=-f(x+1)

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Solution for k(x)=-f(x+1) equation: 


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

Multiply k * x
kx = -1f(x + 1)

Reorder the terms:
kx = -1f(1 + x)
kx = (1 * -1f + x * -1f)
kx = (-1f + -1fx)

Solving
kx = -1f + -1fx

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Divide each side by 'x'.
k = -1fx-1 + -1f

Simplifying
k = -1fx-1 + -1f

Reorder the terms:
k = -1f + -1fx-1

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