Table of Contents
Inverse Functions
A function starts with a value then performs some operation on it and the created output leads to the answer. The inverse function starts with the output answer then performs some operation on it and brings us back to the starting value. An inverse function basically interchanges the first and second elements of each pair of the original function. Inverse Functions – Definition Types and Examples with Solution.
For example, consider that a graph of a function has (a and b) as its points, the graph of an inverse function will have the points (b and a ). An inverse function is written as f−1(x)
Let us take another example, consider f(x) = 3x – 6. What happens to x? We first multiply by 3 and then subtract 6 from the result. But in the reverse function, we follow the steps backward by first adding 6 to undo the subtraction and then divide it by 3 to undo the multiplication.
How to find the Inverse of a Function
Since we now know what an inverse function is, wouldn’t you want to know how to solve inverse functions? What are we waiting for then? Let’s unwrap the mystery.
There are three methods to find the inverse of a function.
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Simply swapping the ordered pairs
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Solve it algebraically
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Using A graph
Example 1) Find the Inverse Function
The inverse function of is .
To find the inverse function, we must first determine its function’s inverse relation. We do this by solving for y in terms of x.
Next, we must determine the function’s inverse function’s domain and range.
The inverse function’s domain is the set of all x-values for which the function’s original relation is true. The inverse function’s range is the set of all y-values for which the inverse function is also true.
In this example, the inverse function’s domain is all real numbers except for x = 2 and the inverse function’s range is all real numbers except for y = 1.
Inverse Functions – Definition Types and Examples with Solution.
