How to Find the Inverse of a Function?
To find the inverse of a function, we need to follow the following steps:
Step 1: Substitue f(x) in the given function by “y”.
Step 2: Solve for “x” for the newly formed equation.
Step 3: Switch the positions of “x” and “y”.
Step 4: Substitute the y with notation of inverse function f -1(x).
Example: Find the inverse of f(x) = 6x + 10.
Solution:
We know, f(x) = 6x + 10. Let’s substitute y in place of f(x).
y = 6x + 10
⇒ y – 10 = 6x
⇒ x = (y – 10)/6
⇒ y = (x – 10)/6
⇒ f -1(x) = (x – 10)/6
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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