Find the domain and range of f(x)=log(2x-1)

Domain: The expression 2x-1 inside the logarithm must be positive, meaning 2x-1 > 0. Solving for x, we get x > 1/2. Therefore, the domain of f(x) is (1/2, ∞).

Range: Since logarithm is an increasing function, the range of f(x) is the same as the range of g(x) = 2x-1. As x varies over (1/2, ∞), g(x) varies over (0, ∞). Therefore, the range of f(x) is (-∞, ∞).

Did you know?

Did you know that when finding the domain and range of a logarithmic function, it's important to consider the restrictions imposed by the logarithm itself? For the function f(x) = log(2x-1), the domain is determined by the argument of the logarithm, which in this case is 2x-1. To ensure that the argument remains positive, we set 2x-1 > 0. Solving this inequality gives us x > 1/2, meaning that the domain of f(x) is all real numbers greater than 1/2. As for the range, it is the set of all possible output values of the function. For logarithmic functions, their range is determined by the nature of logarithms. In this case, the range is all real numbers, as the logarithm of any positive number is defined. However, since the function is defined only for x greater than 1/2, the range is restricted to all real numbers for which the logarithm is defined, but greater than or equal to zero. So, for f(x)=log(2x-1), the range is [0, ∞).