Final answer:
The zeros of the function f(x) are the values x = 1 and x = -1, which are found by setting the numerator (x - 1)(x + 1) equal to zero. These correspond to the options C and E.
The correc answer is C.
Step-by-step explanation:
The question asks for the zeros of the function f(x) = (x−1)(x+1) /6(x−4)(x+7). To find the zeros of this function, we look for the values of x that make the numerator equal to zero, because these are the points at which the function crosses or touches the x-axis. We do not need to consider the denominator when looking for zeros because the fraction is undefined at those points, and they are not included as zeros of the function.
The numerator is (x - 1)(x + 1), which can be set to zero to find the x-values. Setting each factor equal to zero gives the equations x - 1 = 0 and x + 1 = 0, which have solutions x = 1 and x = -1, respectively.
Therefore, the zeros of the function are 1 and -1, corresponding to options C and E.