find the values of a and b that make f continuous everywhere

Question

Answer 1

a= 1/3, b= 2/3

let x=-2

x+2a = 3ax +b

-2+2a =-6a +b

8a = 2+b multiply by 3

24a = 6+3b Equation I

let x =1

3ax+b = 3x-2b

3a +b = 3-2b

3a = 3-3b Equation II

add Equation I and Equation II to get

27a = 9

a = 1/3

substitute 1/3 for a into Equation II

3(1/3) = 3-3b

3b = 2

b = 2/3