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Simplifying (fg)(x) = (3x2 + 11x + 8)(x + 1) Multiply fg * x fgx = (3x2 + 11x + 8)(x + 1) Reorder the terms: fgx = (8 + 11x + 3x2)(x + 1) Reorder the terms: fgx = (8 + 11x + 3x2)(1 + x) Multiply (8 + 11x + 3x2) * (1 + x) fgx = (8(1 + x) + 11x * (1 + x) + 3x2 * (1 + x)) fgx = ((1 * 8 + x * 8) + 11x * (1 + x) + 3x2 * (1 + x)) fgx = ((8 + 8x) + 11x * (1 + x) + 3x2 * (1 + x)) fgx = (8 + 8x + (1 * 11x + x * 11x) + 3x2 * (1 + x)) fgx = (8 + 8x + (11x + 11x2) + 3x2 * (1 + x)) fgx = (8 + 8x + 11x + 11x2 + (1 * 3x2 + x * 3x2)) fgx = (8 + 8x + 11x + 11x2 + (3x2 + 3x3)) Combine like terms: 8x + 11x = 19x fgx = (8 + 19x + 11x2 + 3x2 + 3x3) Combine like terms: 11x2 + 3x2 = 14x2 fgx = (8 + 19x + 14x2 + 3x3) Solving fgx = 8 + 19x + 14x2 + 3x3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'gx'. f = 8g-1x-1 + 19g-1 + 14g-1x + 3g-1x2 Simplifying f = 8g-1x-1 + 19g-1 + 14g-1x + 3g-1x2 Reorder the terms: f = 19g-1 + 8g-1x-1 + 14g-1x + 3g-1x2
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