Inverses of Common Functions
The table given below describes the inverses of some common functions which may come in handy while calculating the inverses for complex functions.
The following table represents the function, its inverse, and its corner cases where corner cases describe the values which are not allowed as input to the inverse of the function.
| Function | Inverse | Corner Cases |
|---|---|---|
xn | Negative values are not allowed when n is even | |
ax | logax | x > 0 and a > 0 |
sin(x) | sin-1(x) | Only values between -1 to 1 are allowed |
cos(x) | cos-1(x) | Only values between -1 to 1 are allowed |
tan(x) | tan-1(x) | — |
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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