Suppose g(x)=f(1−x) for all x, lim x→1^+ f(x)=4, and lim x→1^− f(x)=6. Find lim x→0^+ g(x) and lim x→0^− g(x).

A limit describes the behavior of a function as its input approaches a certain value. In this context, we analyze the limits of the function f(x) as x approaches 1 from the right (1^+) and from the left (1^-). Understanding limits is crucial for determining the values of g(x) at specific points, especially when dealing with piecewise functions or functions defined in terms of others.

Function composition involves combining two functions where the output of one function becomes the input of another. Here, g(x) is defined as f(1−x), which means we need to evaluate f at the point (1−x) to find g's limits. This concept is essential for transforming the limits of f into the limits of g, particularly as x approaches 0.

One-sided limits refer to the value that a function approaches as the input approaches a specific point from one side only, either from the left (−) or the right (+). In this problem, we need to find the one-sided limits of g(x) as x approaches 0, which requires us to consider how f behaves as its argument approaches 1 from both sides, thus impacting the limits of g.