Table of Contents
What is Inverse?
Inverse in Maths: In mathematics, inverse refers to a function that “undoes” another function. The inverse function is usually denoted by the symbol ” ” and is usually read ” ” or ” ” (the function ” “).
For example, the square root function is the inverse of the square function. The square function takes a number and returns the number multiplied by itself. For example, if you take the number 4, the square function would return 16. The square root function, on the other hand, takes a number and returns the number that, when multiplied by itself, would give you the original number. So, for the number 16, the square root function would return 4.
Inverse Operation in Addition
Just as addition is the inverse of subtraction, addition is also the inverse of multiplication. This is because addition and multiplication are both commutative operations. This means that the order of the numbers being operated on does not affect the result.
Inverse Operation on Subtraction
To invert a subtraction, one must first undo the subtraction. This is done by adding the numbers together that were subtracted. Once this is done, the inverse of subtraction is division. Dividing the number that was added back together by the number that was originally subtracted will give the inverse of subtraction.
Inverse Operation on Multiplication
To divide two numbers, divide the first number by the second number.
Inverse Operation on Division
Multiplication is the inverse operation on division.
The Inverse of a Trigonometric Function
- The inverse of a trigonometric function is a function that “undoes” the original function. This means that it takes the input and outputs the original function’s output’s inverse.
- For example, the inverse of the sin function is the arcsin function. This function takes an input and outputs the angle that is the inverse of the input.
The Inverse of an Exponential Function
The inverse of an exponential function is a function that “undoes” the exponential function. It is the function that maps a number to the number that is the inverse of its exponential function.
Problems on Inverse Functions
Inverse functions are a way of undoing or reversing the effect of a function. If you know how to solve for inverse functions, you can use them to solve problems.
Inverse Functions
1. Given the function \(f(x)=x^{2}+4x+3\), find the inverse function.
The inverse function is \(g(x)=\frac{x}{2}-3\).
2. Given the function \(f(x)=x^{3}-4x^{2}+5x+6\), find the inverse function.
The inverse function is \(g(x)=\frac{x}{3}+2\).
