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Simplifying (fg)(x) = (5x2 + -4x)(x2 + -1x + 3) Multiply fg * x fgx = (5x2 + -4x)(x2 + -1x + 3) Reorder the terms: fgx = (-4x + 5x2)(x2 + -1x + 3) Reorder the terms: fgx = (-4x + 5x2)(3 + -1x + x2) Multiply (-4x + 5x2) * (3 + -1x + x2) fgx = (-4x * (3 + -1x + x2) + 5x2 * (3 + -1x + x2)) fgx = ((3 * -4x + -1x * -4x + x2 * -4x) + 5x2 * (3 + -1x + x2)) fgx = ((-12x + 4x2 + -4x3) + 5x2 * (3 + -1x + x2)) fgx = (-12x + 4x2 + -4x3 + (3 * 5x2 + -1x * 5x2 + x2 * 5x2)) fgx = (-12x + 4x2 + -4x3 + (15x2 + -5x3 + 5x4)) Reorder the terms: fgx = (-12x + 4x2 + 15x2 + -4x3 + -5x3 + 5x4) Combine like terms: 4x2 + 15x2 = 19x2 fgx = (-12x + 19x2 + -4x3 + -5x3 + 5x4) Combine like terms: -4x3 + -5x3 = -9x3 fgx = (-12x + 19x2 + -9x3 + 5x4) Solving fgx = -12x + 19x2 + -9x3 + 5x4 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'gx'. f = -12g-1 + 19g-1x + -9g-1x2 + 5g-1x3 Simplifying f = -12g-1 + 19g-1x + -9g-1x2 + 5g-1x3
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