f(X) = 2x^2-8/x-2 7 if x=2 a=2 find the function is continuous at a

Question

show that the function is not continuous at a

f(X) = 2x^2 - 8/x -2  7  if  x = 2  a =2

Answer 1

f(x)=(2x²-8)(x-2)=2(x-2)(x+2)/(x-2)=2(x+2), provided x≠2. So in the limit as x➝a, when a=2, f(x)➝8. The function is not defined at x=2 because we have 0/0 when the function is evaluated. There is a hole at x=2, making it undefined and therefore discontinuous.