Question

If f(x) = x² – 1. Find 

(i) f(x) = x² – 1, 

(ii) fofof

Answer 1

(i) f(x) = x² – 1

fof(x) = f(fx)) = f(x² – 1) 

= (x² – 1)² – 1; 

= x⁴ – 2x² + 1 – 1 

= x⁴ – 2x²

(ii) fofof = f o f(f(x)) 

= f o f (x⁴ – 2x²) 

= f(f(x⁴ – 2x²)) 

= (x⁴ – 2x²)² – 1 

= x⁸ – 4x⁶ + 4x⁴ – 1