Finding the image of the straight line with an equation under a transformation.

A transformation is described through the equation TX+B=X^1

where T=⎡4 0⎤ and B= ⎡-1⎤

⎣0 2⎦ ⎣ 4⎦

Find the image of the curve with equation y=-2x^3+6x under the transformation.

I know how to work out these types of questions when the equation is T(X+B)=X^1, but I'm just not to sure how much differently I will need to do the question.

This is what I was doing:

T^-1*T(X+B)=T^-1*X^1

X+B=T^-1*X^1

and X=T^-1*X^1-B

Therefore you then sub in your matrixes. Once you get an equation for x and y, you then sub them into the straight line equation etc.

Does anyone know if that is the right method?

Thanks in advance.