Question

A function f is defined by f(x) = 3 – 2x. Find x such that f(x²) = (f(x))²

Answer 1

f(x) = 3 – 2x

f(x²) = 3 – 2 (x²)

= 3 – 2x²

(f(x))² = (3 – 2x)²

= 9 + 4x² – 12x

But f(x²) = (f(x))²

3 – 2x² = 9 + 4x² – 12x

–2x² – 4x² + 12x + 3 – 9 = 0

–6x² + 12x – 6 = 0

(÷ by – 6) ⇒ x² – 2x + 1 = 0

(x – 1) (x – 1) = 0

x – 1 = 0 or x – 1 = 0

x = 1

The value of x = 1