If f :R → R is defined by f (x) = x 2 – 3x + 2, write f (f (x)).

Question

Philoid · Accepted Answer

We have,

f(x) = x² – 3x + 2

∴ f(f(x)) = f (x² – 3x + 2)

= (x² – 3x + 2)² – 3(x² – 3x + 2) + 2

= x⁴ + 9x² + 4 – 6x³ – 12x + 4x² – 3x² + 9x – 6 + 2

= x⁴ – 6x³ + 10x² – 3x

⇒ f(f(x)) = x⁴ – 6x³ + 10x² – 3x