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Simplifying f(x + 5) = f(3x) Reorder the terms: f(5 + x) = f(3x) (5 * f + x * f) = f(3x) (5f + fx) = f(3x) Remove parenthesis around (3x) 5f + fx = f * 3x Reorder the terms for easier multiplication: 5f + fx = 3f * x Multiply f * x 5f + fx = 3fx Solving 5f + fx = 3fx Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-3fx' to each side of the equation. 5f + fx + -3fx = 3fx + -3fx Combine like terms: fx + -3fx = -2fx 5f + -2fx = 3fx + -3fx Combine like terms: 3fx + -3fx = 0 5f + -2fx = 0 Factor out the Greatest Common Factor (GCF), 'f'. f(5 + -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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing f to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Add '2x' to each side of the equation. -2x + 2x = -5 + 2x Combine like terms: -2x + 2x = 0 0 = -5 + 2x Simplifying 0 = -5 + 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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