If f(x)= array cl .x²-(a+2) x+a ) x-2 & x 2 2 & , x=2 array . is continuous at x=2 , then the value of a is

Step-by-step solution

Given, f ( x )= array cc x ²-( a +2) x + a x -2 , & x 2 2 & , x=2 array . aligned & _ x 2 x²-(a+2) x+a x-2 &= _ x 2 2 x-(a+2) 1 (by L. Hospital's rule) &=2 2-a-2 &=2-a aligned Since, f(x) is continuous at x=2 , therefore _ x 2 f(x)=f(2) aligned & 2-a &=2 & a &=0 . aligned