f(x) =

x^{2}− 4x− 2if x< 2ax^{2}−bx+ 3if 2 ≤ x< 34 x−a+bif x≥ 3

OK guys so I'm having trouble with this, it includes a lot of algebra steps but I'll put some of them to show that I DID attempt it several times, not sure if I'm just tired or I messed up at some point....

I factored out at the start of coarse...

(x-2)(x+2)/ (x-2) = ax^2 - bx + 3 -----> (2+2) = a(2)^2-b(2)+3

4 = 4a - 2b +3

4 - 3 = 4a - 2b

1 = 4a - 2b

1+2b/4 = 4a/4

1/4+1/2b = a

ax^2 -bx + 3 = 4x - ab

a(3)^2 - b(3) +3 = 4(3) - a + b

9a + a - 3b - b = 12- 3

10a - 4b = 9

10(1/4 + 1/2b) - 4b = 9

5/2 + 5b - 4b = 9

5/2 - 1b = 9

-1b = 13/2

= -13/2

1/4 + 1/2(-13/2) = a

1/4 + (-13/4) = a

- 3 = a

a = -3 b = -13/2