Consider the function f(x)= array ccc a x-2 & for & -2 x -1 -1 & for & -1 x 1 a+2(x-1)^2 & for & 1 x 2 array . What is the value of a for which f(x) is continuous at x=-1 and x =1 ?

Step-by-step solution

f(x)= array cc a x-2 & -2 x -1 -1 & -1 x 1 a+2(x-1)^2 & 1 x 2 array . if f(x) is continuous at x=-1 then, _ x -1 (a x-2)= _ x -1 (-1) aligned & a (-1)-2=-1 & a =-1 aligned if f(x) is continuous at x=1 then, _ x 1 a+2(x-1)^2= _ x 1 -1 aligned & a +2(1-1)^2=-1 & a =-1 aligned