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Simplifying f(n) = f(n + -1) + -1f(n + -2) Multiply f * n fn = f(n + -1) + -1f(n + -2) Reorder the terms: fn = f(-1 + n) + -1f(n + -2) fn = (-1 * f + n * f) + -1f(n + -2) fn = (-1f + fn) + -1f(n + -2) Reorder the terms: fn = -1f + fn + -1f(-2 + n) fn = -1f + fn + (-2 * -1f + n * -1f) fn = -1f + fn + (2f + -1fn) Reorder the terms: fn = -1f + 2f + fn + -1fn Combine like terms: -1f + 2f = 1f fn = 1f + fn + -1fn Combine like terms: fn + -1fn = 0 fn = 1f + 0 fn = 1f Solving fn = 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. -1f + fn = 1f + -1f Combine like terms: 1f + -1f = 0 -1f + fn = 0 Factor out the Greatest Common Factor (GCF), 'f'. f(-1 + n) = 0Subproblem 1
Set the factor 'f' equal to zero and attempt to solve: Simplifying f = 0 Solving f = 0 Move all terms containing f to the left, all other terms to the right. Simplifying f = 0Subproblem 2
Set the factor '(-1 + n)' equal to zero and attempt to solve: Simplifying -1 + n = 0 Solving -1 + n = 0 Move all terms containing f to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + n = 0 + 1 n = 0 + 1 Combine like terms: 0 + 1 = 1 n = 1 Add '-1n' to each side of the equation. n + -1n = 1 + -1n Combine like terms: n + -1n = 0 0 = 1 + -1n Simplifying 0 = 1 + -1n The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
f = {0}
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