# Inverse Function – Definition With Examples

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## Definition of Inverse?

In mathematics, the word inverse refers to the opposite of another operation.

Let us look at some examples to understand the meaning of inverse.

Example 1:

The addition means to find the sum, and subtraction means taking away. So, subtraction is the opposite of addition. Hence, addition and subtraction are opposite operations.  We may say, subtraction is the inverse operation of addition.

Example 2:

However, the division is repeated subtraction. The same number gets subtracted repeatedly.  So, division is the opposite of multiplication. Hence, multiplication and division are opposite operations. We may say, division, is the inverse operation of multiplication.

So, we see that multiplication and division are inverses of each other.

## Multiplicative Identity:

A multiplicative identity is a number that when multiplied by any non-zero number gives the same number as the product.

For example, if a is any non-zero number, then multiplying a  by 1 gives the product as the number itself.

a × 1 = a

Therefore, 1 is the multiplicative identity.

## Multiplicative Inverse:

A multiplicative inverse is a number which when multiplied by a number gives 1 (multiplicative identity) as the product.

If a is any non-zero number, then multiplying a by what number gives the product as 1?

a × ? = 1

As, aa = 1, we need a number in which a is in the denominators place. We have a in the numerator. So, we keep 1 is the numerator of this number and get 1a.

a × 1a = 1

So, 1a is the multiplicative inverse of a.

Multiplicative inverse is also called a reciprocal.

Reciprocal of a number is obtained by interchanging its numerator and denominator.

The multiplicative inverse of a is 1and multiplicative inverse of a fraction  ab is ba

## Practice Problems

1

### Which of the following would be the multiplicative identity for the decimal number 2.35?

0
1
2.35
235/100
CorrectIncorrect
The multiplicative identity is a quantity which when multiplied by any number gives the product as the number itself. The only number that follows this condition is the number 1.
2

### Identify the related division sentence for 5 × 2 = 10.

10 ÷ 2 = 5
5 ÷ 1 = 5
20 ÷ 5 = 4
2 ÷ 1 = 2
CorrectIncorrect
Correct answer is: 10 ÷ 2 = 5
Here, as per the given multiplication expression, 5 and 2 are the factors of 10.
Hence 10 divided by 2 equals 5 or 10 divided by 5 equals 2 are the only plausible division sentences for the given equation.
3

### What is the multiplicative inverse of 2/3?

1/3
1
2/3
3/2
CorrectIncorrect
2/3 × 3/2= 1.
Hence, the multiplicative inverse of 2/3 = 3/2.
4

1
2/7
1/7
7
CorrectIncorrect