If T : P1 rightarrow P1 is a linear transformation such that T(1 + 4x) = -4 - 2x and T(3 + 11 x) = - 4 - 2x,then T(-3 - 5x) =. Solution T(1+4x)=-4-2x T(3+11x)=-4-2x suppose -3-5x=a(1+4x)+b(3+11x) -3-5x=(a+3b)+(4a+11b)x compare coefficient of x and constant term on both sides we get, -3=a+3b ..................(1) -5=4a+11b .....................(2) multiply (1) by 4 and subtract it from (2) we get, b=-7 putting value of b in (1) we get a=18 -3-5x=18(1+4x)-7(3+11x) T(-3-5x)=T(18(1+4x)-7(3+11x)) T(-3-5x)=18T((1+4x))-7T((3+11x)) ....since T(ax+by)=aT(x)+bT(y) T(-3-5x)=18(-4-2x)-7(-4-2x) T(-3-5x)=-72-36x+28+14x T(-3-5x)=-44-22x.