Throughout mathematics, a multiplicative inverse or reciprocal for the number x is also represented as $\frac{1}{x}$ or $x^-1$ can be various which once multiplied by cycles yields the multiplicative detection 1.

The particular multiplicative inverse regarding any fraction a/b will likely be $\frac{b}{a}$. For the multiplicative inverse of any real number divide 1 from the number.

An inverse function generally is a function that "reverses" another function if the function f officially used on an input x gives a consequence of y then applying their own inverse function g to y improves the result x, in addition and vice versa. once i. e., f(x) = y if for if g(y) = x. If any sum is given then it may easily find the exact multiplicative inverse on the number.

## definition

An additional name for Reciprocal is the multiplicative inverse.
Whenever you multiply a variety by its "Multiplicative Inverse" you have 1.

Example: 8 × ($\frac{1}{8}$) = 1
Your notation $x^-1$ may also be used for the inverse function, which usually seriously isn't comparable to the particular multiplicative inverse..

As an example, $\frac{1}{sin x}$ = $(sin x)^-1$ is completely different from the inverse associated with sin x, denoted sin$^-1$ x as well as arcsin x.

## Steps

Multiplicative inverse, a set of numbers which when multiplied yield the multiplicative identity, 1.
If an inverse function exists for a given function f, it is unique: it must be the inverse relation.
Multiplicative Inverse steps are given below.

Step 1:
Write the reciprocal of the given number.

Multiplicative inverse of a number n =  $n^{-1}$(or) $\frac{1}{n}$ .

Step 2:

Now, check the product of number n and its multiplicative inverse $\frac{1}{n}$ should be 1, that is:

n $\times$ $\frac{1}{n}$=1.

We can even find the multiplicative inverse of a rational number by reciprocating the given rational number.

For Example: consider a rational number say $\frac{4}{5}$

Its multiplicative inverse is $\frac{5}{4}$ by changing the numerator to denominator and vice versa.

## multiplicative inverse of a negative number

The product of a negative number and its reciprocal equals 1. If the number is negative then the reciprocal must also be negative to produce a product of +1.

Example: The reciprocal of -4 is -$\frac{1}{4}$.

The reciprocal of -$\frac{2}{3}$ is -$\frac{3}{2}$.

The reciprocal of -1 is -1.

The particular reciprocal of x is $\frac{1}{x}$. Quite simply, a reciprocal is really a fraction flipped.

Multiplicative inverse means exactly the same thing as reciprocal.

The product of a number and its multiplicative inverse is 1. Observe that $\frac{3}{5}$.$\frac{5}{3}$ = 1.