Find the domain of the function. \[ f(x)=\frac{8}{x^{2}-7 x-98} \] What is the domain of \( f \) ?

The domain of a function consists of all the input values (x-values) for which the function is defined. In this function   f(x) = 8/(x² - 7x - 98), the only restriction comes from the denominator. The function is undefined when the denominator is zero. So, we need to find the values of x such that   x² - 7x - 98 = 0. To solve this quadratic equation, we can factor it. We look for two numbers that multiply to -98 and add to -7. The numbers -14 and 7 work because:   (-14) × 7 = -98  and  (-14) + 7 = -7. Thus, the quadratic factors as:   (x - 14)(x + 7) = 0. Setting each factor equal to zero gives:   x - 14 = 0  ⟹ x = 14,   x + 7 = 0  ⟹ x = -7. Since the function is undefined when the denominator is zero, we must exclude x = 14 and x = -7 from the domain. Hence, the domain of f is all real numbers except x = -7 and x = 14. In interval notation, the domain is written as:   (-∞, -7) ∪ (-7, 14) ∪ (14, ∞).