Final answer:
The function f(x) has a discontinuity at x = 3 after simplifying the equation by canceling out the (x+7) term from both numerator and denominator.
Step-by-step explanation:
The question pertains to finding discontinuities in the given function f(x) = ((x+7)(2x-1))/((x+7)(x-3)). To determine the discontinuities of f(x), we need to identify any x values that would cause the denominator to be zero, as these are the values where the function is not defined. In the given function, f(x) is undefined when x = -7 and x = 3, because these values would make the denominator equal to zero. However, it should be noted that the (x+7) term appears both in the numerator and the denominator, and it will cancel out, leaving us with f(x) = (2x-1)/(x-3). Thus, the only real discontinuity is at x = 3, because that is where the function is undefined after the simplification.