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Simplifying f(x) = f(x + 1) + 100 Multiply f * x fx = f(x + 1) + 100 Reorder the terms: fx = f(1 + x) + 100 fx = (1 * f + x * f) + 100 fx = (1f + fx) + 100 Reorder the terms: fx = 100 + 1f + fx Add '-1fx' to each side of the equation. fx + -1fx = 100 + 1f + fx + -1fx Combine like terms: fx + -1fx = 0 0 = 100 + 1f + fx + -1fx Combine like terms: fx + -1fx = 0 0 = 100 + 1f + 0 0 = 100 + 1f Solving 0 = 100 + 1f Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-1f' to each side of the equation. 0 + -1f = 100 + 1f + -1f Remove the zero: -1f = 100 + 1f + -1f Combine like terms: 1f + -1f = 0 -1f = 100 + 0 -1f = 100 Divide each side by '-1'. f = -100 Simplifying f = -100
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