For AI agents: use /llms.txt for the Nakafa content index.
You often translate words or sentences from English to Indonesian, for example, when watching movies or reading news. This translation process is similar to how a function works: there is an input (English word) and an output (Indonesian word).
Consider the following illustration:
Here, the "Translation Machine" acts like a function that transforms "Mathematics" (input) into "Matematika" (output).
Now, what if we want to do the reverse? Translate "Matematika" back into "Mathematics"?
This reverse process is the basis of the inverse function concept.
An inverse function is a function that "reverses" the operation of an initial function. If function maps element from domain to element in codomain , then its inverse function, denoted as (read "f inverse"), maps element from back to element in .
Mathematically:
In other words, if changes to , then changes back to . The inverse function "undoes" the effect of the original function.
Important: The notation does not mean (multiplicative inverse or reciprocal). It is special notation for the inverse function.
Not all functions have an inverse function. For a function to have an inverse function , the function must be bijective. A bijective function is both injective (one-to-one) and surjective (onto).
If function is not bijective, its inverse relation might exist, but that relation will not be a function.
To find the formula for the inverse function from a function , you can follow these steps:
Example:
Find the inverse function of .
Replace with :
Swap and :
Solve for :
Replace with :
So, the inverse function of is .
The graph of the inverse function is a reflection of the graph of the original function across the line .
For example, let's look at the graph of , its inverse , and the identity line .
