Question

dada a função f(x)= x2+4x+4 calcule f(f(f(x)))?

Answer 1

f(x) =x2+4x+4= (x+2)^2
f(f(x))= ((x+2)^2+2)^2
f(f(f(x)))=(((x+2)^2+2)^2+2)^2
=((x+2)^4 + 4(x+2)+2)^2
=(x^4+8x^3+28x^2+48x+38)^2
=x^8+16x^7+120 x^6+ 544  x^5+ 1628 x^4+ 3296 x^3+ 4432 x^2+3648 x+ 1444