Let f (x)= cases x^4-5 x^2+4 |(x-1)(x-2)| & , x 1,2 6 & , x=1 12 & , x=2 cases then f (x) is continuous on the set

Step-by-step solution

Continuity analysis for f(x)= cases x^4-5 x^2+4 |(x-1)(x-2)| & , x 1,2 6 & , x=1 12 & , x=2 cases The expression simplifies to (x-1)(x+1)(x-2)(x+2) |x-1||x-2| for x 1,2 . At x=1 , the left-hand limit evaluates to (1+1)(1+2) = 6 , while the right-hand limit gives -(1+1)(1+2) = -6 . The limit does not exist, so f is discontinuous at x=1 . At x=2 , the left-hand limit yields -(2+1)(2+2) = -12 , and the right-hand limit gives (2+1)(2+2) = 12 . The limit does not exist, confirming discontinuity at x=2 . For x 1,2 , f is