Question

An operation * find the inverse of an element x£R

Answer 1

To find the inverse of an element \( x \) in the context of real numbers \( \mathbb{R} \), we first need to clarify the type of operation we're discussing, as "inverse" can have different meanings depending on the type of operation (addition, multiplication, etc.).

### 1. **Multiplicative Inverse**
The multiplicative inverse of a number \( x \) (where \( x \neq 0 \)) is defined as the number that, when multiplied by \( x \), yields 1. Mathematically, it is expressed as:

\[
x^{-1} = \frac{1}{x}
\]

For example, the multiplicative inverse of \( 5 \) is:

\[
5^{-1} = \frac{1}{5}
\]

### 2. **Additive Inverse**
The additive inverse of a number \( x \) is defined as the number that, when added to \( x \), yields 0. Mathematically, it is expressed as:

\[
-x
\]

For example, the additive inverse of \( 5 \) is:

\[
-5
\]

### Summary
- **Multiplicative Inverse of \( x \)**: \(\frac{1}{x}\) (for \( x \neq 0 \))
- **Additive Inverse of \( x \)**: \(-x\)

If you have a specific operation in mind or a specific context (like matrices or groups), please provide more details for a tailored explanation!