# What Does Input and Output Mean in Math?

In mathematical equations known as functions, input and output replace the variables. Input is the variable that is known, and output is the solution. Utilize functions whenever a variable (x) transforms to equal a new variable (y).

In college-level algebra and trigonometry, functions are a type of mathematical language used to illustrate the relationship between two variables. A function example is f(x) = x + 4. The answer, f(x), is also the output variable y. To answer the equation, simply select a value for the input variable x. The connection is x plus 4. If a problem-solver needs to determine the output if the input value is 5, the resulting equation is f(5) = 5 + 4. The solution to the issue is f(5) = 9 and the output is 9. This is a relatively simple example; nevertheless, as the relationship between two variables becomes more involved in advanced mathematics, functions can become extremely complex problems. In order to simplify these challenges, functions adhere to two strict rules. The function must be a valid relationship between all inputs and outputs, meaning that for each input there must be exactly one output, and it must function for all input values. This is what constitutes the input-output relationship as a function.