Question

If f: R → R is described by f(x) = x2 − 3x + 2, determine f(f(x)).​

Answer 1

Answer:

x4 – 6x3 + 10x2 – 3x

Step-by-step explanation:

f(x) = x2 – 3x + 2 ∴ f (f (x)) = f (y) where y = x2 – 3x + 2 = y2 – 3y + 2 = (x2 – 3x + 2)2 – 3(x2 – 3x + 2) + 2 = x4 + 9x2 + 4 – 6x3 + 4x2 – 12x – 3x2 + 9x – 6 + 2 = x4 – 6x3 + 10x2 – 3x