Answer:
The function f(x) = (x^2 + 9x + 14) / (x + 7) has a singularity at x = -7. It is an isolated singularity, which means that there are no other singularities in the neighbourhood of x = -7.
In order to understand the type of discontinuity that is created by this singularity, we need to evaluate the limits of the function as x approaches -7.
As x approaches -7 from the left side (x < -7), the function becomes infinite and unbounded. This means that the limit does not exist as x approaches -7 from the left.
As x approaches -7 from the right side (x > -7), the function approaches a limit of 0. This means that the function is continuous at x = -7 from the right.
Therefore, f(x) has a jump/discontinuity at x = -7, and the discontinuity is of the infinite type.
Explanation:
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