F (x) + x^2+3x+2 is shifted 2 units left. the result is g (x). what is g (x) ?

Adding 2 to all the x's shifts the function left.

g (x) = (x+2) ² + 3 (x+2) + 2

simplify it a bit ...

g (x) = (x+2) ² + 3x + 6 + 2

g (x) = (x+2) ² + 3x + 8

g (x) = x² + 4x + 4 + 3x + 8

g (x) = x² + 7x + 12