Find \( f(g(x)) \) and \( g(f(x)) \) and determine whether the pair of functions \( f \) and \( g \) are inverses of each other. \( f(x)=x \) and \( g(x)=x \) \( f(g(x))=\square \)

To find \( f(g(x)) \) and \( g(f(x)) \), we need to substitute the expressions for \( f(x) \) and \( g(x) \) into each other. Given: \( f(x) = x \) \( g(x) = x \) 1. Find \( f(g(x)) \): Substitute \( g(x) \) into \( f(x) \): \( f(g(x)) = f(x) = x \) 2. Find \( g(f(x)) \): Substitute \( f(x) \) into \( g(x) \): \( g(f(x)) = g(x) = x \) Now, we need to determine whether the pair of functions \( f \) and \( g \) are inverses of each other. For two functions to be inverses of each other, the composition of the functions in both orders should result in the original input. In this case, both \( f(g(x)) \) and \( g(f(x)) \) result in \( x \), which means the pair of functions \( f \) and \( g \) are inverses of each other.