👉 In mathematics, a non-substitutionally defined function is a mathematical function that does not have any inverse. In other words, a non-substitutionally defined function does not have an output value that can be paired with an input value to produce a unique output value. For example, consider the function f(x) = 2x + 1. This function has no inverse since for every x in its domain (the set of all real numbers), there is only one y that satisfies the equation