ITENCE Functions \( f \) and \( g \) are inverses of each other provided that \( f(g(x))=\square \) and \( g(f(x))=\square \)

When functions \( f \) and \( g \) are inverses, they essentially "undo" each other's effects. This means that when you first apply function \( g \) to \( x \) and then apply function \( f \) to the result, you should end up back at your original input, \( x \). So, we fill in the squares with \( x \): \( f(g(x)) = x \) and \( g(f(x)) = x \). It's like a mathematical game of hide and seek, where each function captures and then reveals the original value! Understanding inverse functions isn’t just theoretical—it has real-world implications, especially in fields like cryptography, computer science, and engineering. For instance, data encryption uses algorithms that rely on inverse functions to secure and then decode information. When you encrypt a message using a specific function, the inverse function provides a way to revert to the original message, keeping your data safe while allowing it to be retrieved accurately!