If f(x)= array cc x-|x| x , & when x < 0 b ( 5 x^2+a, x^2-3 x+2 ), & when 0 x 1 -14, & when x 3 array . is a continuous function on R , then (a, b)=

Step-by-step solution

Given, f(x)= array cc x-|x| x ; & when x < 0 b ( x^2+a ; x^2-3 x+2 ) ; & when 0 x 1 -14 ; & when x 3 array . Since, given f(x) is continuous at x=0 and x=3f(x) is continuous at x=0 . aligned & LHL at x=0= RHL at x=0 & = _ x 0⁻ f(x)= _ x 0⁺ f(x) aligned aligned & = _ x 0⁻ x-|x| x = _ x 0⁺ 5 x^2+a & = _ x 0⁻ x-(-x) x = _ x 0 5 x^2+a & = _ x 0⁻ 2 x x =5(0)^2+a & [ as x < 0, then |x|=-x] & a & 2 aligned f(x) is also continuous at x=3 LHL at (x=3)= RHL at (x=3) aligned & = _ x 3⁻ f(x)= _ x 3⁺ f(x) & = _ x 3⁻ b ( x^2-1 x