Function theory is a branch of mathematics that studies the properties and behaviors of functions, which are relationships between sets of inputs and outputs. It explores how functions can be represented, manipulated, and analyzed, often using concepts from calculus and algebra. In function theory, various types of functions, such as linear functions, polynomial functions, and trigonometric functions, are examined to understand their characteristics. This field is essential in many areas of mathematics and applied sciences, providing tools for modeling real-world phenomena and solving equations.