Question

Answer the following:

If f(x) = 3x⁴ – 5x² + 7 find f(x – 1)

Answer 1

f(x) = 3x⁴ – 5x² + 7

∴ f(x – 1) = 3(x – 1)⁴ – 5(x – 1)² + 7

= 3(x⁴ – ⁴C₁ x³ + ⁴C₂ x² – ⁴C₃ x + ⁴C₄) – 5(x² – 2x + 1) + 7

= 3(x⁴ – 4x³ + 6x² – 4x + 1) – 5(x² – 2x + 1) + 7

= 3x⁴ – 12x³ + 18x² – 12x + 3 – 5x² + 10x – 5 + 7

= 3x⁴ – 12x³ + 13x² – 2x + 5