I) Under the transformation T(x,y) → (x-4,y+2), we have that:

a) T(2,-1)=(2-4,-1+2)=(-2,1)

If a point (x,y) has already been through the transformation, then the previous x-coordinate decreased by 4, and the y-coordinate increased by 2 - hence we perform the opposite operations; i.e.:

b) (3,5)=(x-4,y+2); equating x-coordinates: 3=x-4, or x=7

equating y-coordinates: 5=y+2 or y=3

Hence the pre-image of the point (3,5), was (7,3)

II) Under the transformation T(x,y)→ (x-1,y+2), we have that:

a) T(-2,1)=(-2-1,1+2)=(-3,3)

If a point (x,y) has already been through the transformation, then its x-coordinate has decreased by one, and its y-coordinate has increased by two - so we perform the opposite operations to find the pre-image:

b) (3,2)=(x-1,y+2); equating x-coordinates: 3=x-1, or x=4

equating y-coordinates: 2=y+2, or y=0

Hence the pre-image of (3,2), is the point (4,0)