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Simplifying f(3x + 1) = f(x) Reorder the terms: f(1 + 3x) = f(x) (1 * f + 3x * f) = f(x) (1f + 3fx) = f(x) Multiply f * x 1f + 3fx = fx Solving 1f + 3fx = fx Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-1fx' to each side of the equation. 1f + 3fx + -1fx = fx + -1fx Combine like terms: 3fx + -1fx = 2fx 1f + 2fx = fx + -1fx Combine like terms: fx + -1fx = 0 1f + 2fx = 0 Factor out the Greatest Common Factor (GCF), 'f'. f(1 + 2x) = 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 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -2x 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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