What is the domain of the function \( f(x)=\log _{10}(x+1) ? \)

To find the domain of the function \( f(x) = \log_{10}(x + 1) \), we need to determine when the argument of the logarithm, \( x + 1 \), is positive. That is, we require \( x + 1 > 0 \). Solving this inequality, we get \( x > -1 \). Therefore, the domain of \( f(x) \) is all real numbers greater than \(-1\), which can be expressed in interval notation as \( (-1, \infty) \). Understanding logarithmic functions is super interesting! Did you know that logarithms were invented in the early 17th century by John Napier as a way to simplify complex calculations, especially for astronomers and navigators who had to deal with huge numbers? In practical terms, the logarithm function is widely used in computer science, particularly in algorithms that have logarithmic time complexity, like binary search. This means that as the input size increases, the number of operations grows much more slowly than the size itself—which is quite handy when you need efficiency in your code!