Question

halle la transformacion lineal de t p2 a p2

Answer 1

$T(1)=1+x\to T(a)=aT(1)=a+ax\\ \\ T(x)=3-x^2\to T(bx)=bT(x)=3b-bx^2\\ \\ T(x^2)=4+2x-3x^2\to T(cx^2)=cT(x^2)=4c+2cx-3cx^2\\ \\ \\ T(a+bx+cx^2)=T(a)+T(bx)+T(cx^2)\\ T(a+bx+cx^2)=(a+ax)+(3b-bx^2)+(4c+2cx-3cx^2)\\ \\ \boxed{T(a+bx+cx^2)=(a+3b+4c)+(a+2c)x-(b+3c)x^2}\\ \\ \bold{T(2-2x+3x^2)=8+8x-7x^2}$