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Simplifying f(n) = 2f(n + -1) + 1 Multiply f * n fn = 2f(n + -1) + 1 Reorder the terms: fn = 2f(-1 + n) + 1 fn = (-1 * 2f + n * 2f) + 1 fn = (-2f + 2fn) + 1 Reorder the terms: fn = 1 + -2f + 2fn Solving fn = 1 + -2f + 2fn Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '2f' to each side of the equation. 2f + fn = 1 + -2f + 2f + 2fn Combine like terms: -2f + 2f = 0 2f + fn = 1 + 0 + 2fn 2f + fn = 1 + 2fn Add '-2fn' to each side of the equation. 2f + fn + -2fn = 1 + 2fn + -2fn Combine like terms: fn + -2fn = -1fn 2f + -1fn = 1 + 2fn + -2fn Combine like terms: 2fn + -2fn = 0 2f + -1fn = 1 + 0 2f + -1fn = 1 Reorder the terms: -1 + 2f + -1fn = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 2f + -1fn = 0 The solution to this equation could not be determined.
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