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Simplifying xf(x) = 4f(x + -1) Multiply fx * x fx2 = 4f(x + -1) Reorder the terms: fx2 = 4f(-1 + x) fx2 = (-1 * 4f + x * 4f) fx2 = (-4f + 4fx) Solving fx2 = -4f + 4fx Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '4f' to each side of the equation. 4f + fx2 = -4f + 4f + 4fx Combine like terms: -4f + 4f = 0 4f + fx2 = 0 + 4fx 4f + fx2 = 4fx Add '-4fx' to each side of the equation. 4f + -4fx + fx2 = 4fx + -4fx Combine like terms: 4fx + -4fx = 0 4f + -4fx + fx2 = 0 Factor out the Greatest Common Factor (GCF), 'f'. f(4 + -4x + x2) = 0 Factor a trinomial. f((2 + -1x)(2 + -1x)) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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