Final answer:
The domain of the function is determined by the values that make the denominator of the function non-zero. In this case, the denominator of the function is x² - 5x - 24. The numbers 8 and -3 are not in the domain of the function.
Step-by-step explanation:
The domain of the function is determined by the values that make the denominator of the function non-zero. In this case, the denominator of the function is x² - 5x - 24. To find the values that make the denominator zero, we need to solve the equation x² - 5x - 24 = 0. Factoring the equation, we have (x - 8)(x + 3) = 0, which gives us two solutions: x = 8 and x = -3. Therefore, the numbers 8 and -3 are not in the domain of the function.
The domain of the function, using set notation, is x . This means that the function is defined for all real numbers except 8 and -3.
Learn more about Domain of a Function