Graphs of Inverse Functions
To understand the graph of the inverse function, let’s say we have f(x) = ex and assume it has inverse i.e., g(x). We know that the inverse of an exponential function is a logarithmic function. So, g(x) = logex. The figure below shows the graph for both of the functions.
We can see that both graphs are mirror images of each other with respect to the line y = x. So, we can say that the inverse of a function is a mirror image of the function when seen through the line y = x.
Note: There is no shortcut way to plot the graph of the inverse function if the graph of the original function is not given.
Also read: Graph of inverse trigonometry system
Inverse Functions
Inverse Functions are an important concept in mathematics. To comprehend inverse functions, we can picture a function as a box that takes in inputs and produces outputs. If a function consistently generates a red-colored object as output for any input object, we can identify that box as the initial function. The box that accepts both red and normal-colored objects as inputs and generates the original-colored objects as outputs, is called the inverse of the initial box.
In other words, if a function is an operation that produces an output for each input, the inverse function facilitates the identification of the specific input based on a given output. Let’s learn about inverse functions and all the different associated topics with them.
Table of Content
- What are Inverse Functions?
- How to Find the Inverse of a Function?
- Inverses of Common Functions
- Graphs of Inverse Functions
- Inverse Function Types
- Inverse Trigonometric Function
- Exponential and Logarithm Function
- Inverse Hyperbolic Function
- Inverse Functions Examples
- Inverse Functions Worksheet
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