Final answer:
The function g(x) = log(x² - 49) is defined for x > 7 or x < -7, and it has a constant value of log(15) for all those x values.
Step-by-step explanation:
The function g(x) = log(x² - 49) can be analyzed by considering its domain, ranges, and behavior. The expression inside the logarithm, x² - 49, needs to be greater than zero for the function to be defined. Thus, x² - 49 > 0. By factoring, we find that (x+7)(x-7) > 0. This means that the function is defined for values of x that satisfy x > 7 or x < -7.
For example, if we take the value x = 8, we get g(8) = log(8² - 49) = log(15). Similarly, if we take the value x = -8, we get g(-8) = log((-8)² - 49) = log(15). This indicates that the function will have the same value for these two inputs, and it will continue to have the same value for any x values that satisfy the condition x > 7 or x < -7.
Thus, the function g(x) = log(x² - 49) is defined for x > 7 or x < -7 and it has a constant value of log(15) for all those x values.
Learn more about Understanding the domain and behavior of the function