what are the domain and range of the logarithmic function (f(x)=log_{7}x)? use the inverse function to…

Explanation:

Step1: Recall the definition of domain

The argument of a logarithm must be positive. For (y = \log_{7}x), (x>0). So the domain is the set of all positive real - numbers.

Step2: Find the inverse function

Let (y=\log_{7}x). By the definition of logarithms, the inverse of (y = \log_{7}x) is (x = 7^{y}).

Step3: Determine the range

For the exponential function (x = 7^{y}), (y) can be any real number. Since the range of the inverse function is the domain of the original function and vice - versa, the range of (y=\log_{7}x) is the set of all real numbers.

Answer:

Domain: ((0,+\infty)); Range: ((-\infty,+\infty))