If f(x)= array ll 3 a x-2 b, & x 1 a x+b+1, & x 1 array . and _ x 1 f(x) exists, then the relation between a and b is

Step-by-step solution

Given, f(x)= cases 3 a x-2 b, & x 1 a x+b+1, & x 1 cases aligned & Since, _ x 1 f(x) exist _ x 1⁻ f(x)= _ x 1⁺ f(x) & _ x 1⁻ (a x+b+1)= _ x 1⁺ (3 a x-2 b) & a+b+1=3 a-2 b 2 a-3 b=1 aligned