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Simplifying f(n) = 2f(n + -1) Multiply f * n fn = 2f(n + -1) Reorder the terms: fn = 2f(-1 + n) fn = (-1 * 2f + n * 2f) fn = (-2f + 2fn) Solving fn = -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 = -2f + 2f + 2fn Combine like terms: -2f + 2f = 0 2f + fn = 0 + 2fn 2f + fn = 2fn Add '-2fn' to each side of the equation. 2f + fn + -2fn = 2fn + -2fn Combine like terms: fn + -2fn = -1fn 2f + -1fn = 2fn + -2fn Combine like terms: 2fn + -2fn = 0 2f + -1fn = 0 Factor out the Greatest Common Factor (GCF), 'f'. f(2 + -1n) = 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 '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing f to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Add 'n' to each side of the equation. -1n + n = -2 + n Combine like terms: -1n + n = 0 0 = -2 + n Simplifying 0 = -2 + n 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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