Final answer:
A function is invertible when it is bijective, meaning each output is uniquely linked to one input. Making a function invertible involves finding the inverse process that reverses the effect of the function. In math, this could mean using operations like square roots or logarithms to retrieve the original inputs from the outputs.
Step-by-step explanation:
A function becomes invertible when each output of the function corresponds to exactly one input. In mathematical terms, this means the function must be bijective, which is a combination of being injective (one-to-one) and surjective (onto). To "invert" a function, we are essentially attempting to find a reverse process wherein we can compute the original input given the output.
An example of making a function invertible can be seen with quadratics, such as a to the power of 2. To find a, we would take the square root of both sides of the equation, effectively "undoing" the squaring process. This principle is similar to that of natural log and exponential functions, where one function serves as the inverse of the other.
The concept of a reversible process is also related to inverse processes in physics and chemistry, where a system can return to its initial state without a net change to the system and surroundings.