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Simplifying f(f(x)) = x4 + -20x2 + 90 Multiply f * x f(fx) = x4 + -20x2 + 90 Multiply f * fx f2x = x4 + -20x2 + 90 Reorder the terms: f2x = 90 + -20x2 + x4 Solving f2x = 90 + -20x2 + x4 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f2 = 90x-1 + -20x + x3 Simplifying f2 = 90x-1 + -20x + x3 Reorder the terms: f2 + -90x-1 + 20x + -1x3 = 90x-1 + -90x-1 + -20x + 20x + x3 + -1x3 Combine like terms: 90x-1 + -90x-1 = 0 f2 + -90x-1 + 20x + -1x3 = 0 + -20x + 20x + x3 + -1x3 f2 + -90x-1 + 20x + -1x3 = -20x + 20x + x3 + -1x3 Combine like terms: -20x + 20x = 0 f2 + -90x-1 + 20x + -1x3 = 0 + x3 + -1x3 f2 + -90x-1 + 20x + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 f2 + -90x-1 + 20x + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x-1'. x-1(f2x + -90 + 20x2 + -1x4) = 0Subproblem 1
Set the factor 'x-1' equal to zero and attempt to solve: Simplifying x-1 = 0 Solving x-1 = 0 Move all terms containing f to the left, all other terms to the right. Add '-1x-1' to each side of the equation. x-1 + -1x-1 = 0 + -1x-1 Remove the zero: 0 = -1x-1 Simplifying 0 = -1x-1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(f2x + -90 + 20x2 + -1x4)' equal to zero and attempt to solve: Simplifying f2x + -90 + 20x2 + -1x4 = 0 Reorder the terms: -90 + f2x + 20x2 + -1x4 = 0 Solving -90 + f2x + 20x2 + -1x4 = 0 Move all terms containing f to the left, all other terms to the right. Add '90' to each side of the equation. -90 + f2x + 20x2 + 90 + -1x4 = 0 + 90 Reorder the terms: -90 + 90 + f2x + 20x2 + -1x4 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + f2x + 20x2 + -1x4 = 0 + 90 f2x + 20x2 + -1x4 = 0 + 90 Combine like terms: 0 + 90 = 90 f2x + 20x2 + -1x4 = 90 Add '-20x2' to each side of the equation. f2x + 20x2 + -20x2 + -1x4 = 90 + -20x2 Combine like terms: 20x2 + -20x2 = 0 f2x + 0 + -1x4 = 90 + -20x2 f2x + -1x4 = 90 + -20x2 Add 'x4' to each side of the equation. f2x + -1x4 + x4 = 90 + -20x2 + x4 Combine like terms: -1x4 + x4 = 0 f2x + 0 = 90 + -20x2 + x4 f2x = 90 + -20x2 + x4 Divide each side by 'x'. f2 = 90x-1 + -20x + x3 Simplifying f2 = 90x-1 + -20x + x3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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