Question

Calculati (fof)(0),stiind ca f:R→Rf(x)=2x^2-3x+1

Answer 1

Compunem functia $f(x)=2x^2 -3x + 1$ cu ea insasi:

$f[f(x)]=f(2x^2-3x+1)=2(2x^2-3x+1)^2-3(2x^2-3x+1)+1\\= 2(4x^4-9x^2+1)-6x^2+9x-3+1=\\=8x^4-18x^2+2-6x^2+9x-2=\\=8x^4-24x^2+9x \\\\f[f(x=0)]= 8x0^4 - 24 x 0^2 + 9 x 0 = 0$