Answer:
Option A,B,D
Step-by-step explanation:
For f(x) = (x-1)/(x²-1)
f(x) = (x-1)/(x-1)(x+1)
Therefore hole at x = 1
For f(x) = (x²-9)/(x²+7x+12) = (x-3)(x+3)/(x²+4x+3x+12) = (x-3)(x+3)/(x+3)(x+4)
Common factor (x+3) in numerator and denominator so
Function has hole at x = -3
For f(x) = (x² + 4x + 4)/(x² + 2x - 8) = (x+2)²/(x² +4x -2x -8) = (x+2)²/(x+4)(x-2)
This function has no discontinuity.
For f(x) = (x +7)/(x²+5x-14) = (x+7)/(x² + 7x -2x -14) = (x+7)/(x-2)(x+7)
This function has a hole at x = -7
Option A,B,D have the removable discontinuity.
