If f: R R is defined by aligned & f(x)= array ccc x-2 x^2-3 x+2 & if & x R- 1,2 2 & if & x=1 1 & if & x=2 array . then & _ x 2 f(x)-f(2) x-2 = aligned

Step-by-step solution

Given that aligned & f(x)= array ccc x-2 x^2-3 x+2 , & if & x R- 1,2 2, & if & x=1 1, & if & x=2 array . & _ x 2 f(x)-f(2) x-2 & = _ x 2 x-2 x^2-3 x+2 -1 x-2 & = _ x 2 x-2- (x^2-3 x+2 ) (x-2) (x^2-3 x+2 ) & = _ x 2 -(x-2)^2 (x-2)(x-2)(x-1) & =- _ x 2 1 x-1 =- 1 2-1 =-1 aligned