If `f(x)=x`, the inverse of `f,f^(-1)`, could be represented by

Options

A. `f^(-1)(x)=x`
B. `f^(-1)(x)=1`
C. `f^(-1)(x)=(1)/(x)`
D. `f^(-1)(x)=y`

Explanation

To find the inverse of the function \( f(x) = x \), we can follow these steps:

### Step 1: Replace \( f(x) \) with \( y \)
We start by rewriting the function:
\[ y = f(x) = x \]

### Step 2: Solve for \( x \) in terms of \( y \)
In this case, since \( y = x \), we can directly see that:
\[ x = y \]

### Step 3: Express the inverse function
Now we can express the inverse function. Since we have \( x = y \), we can write:
\[ f^{-1}(y) = x \]
Substituting \( y \) back with \( x \) gives us:
\[ f^{-1}(x) = x \]

### Conclusion
Thus, the inverse of the function \( f(x) = x \) is:
\[ f^{-1}(x) = x \]

### Final Answer
The inverse function \( f^{-1} \) could be represented by \( f^{-1}(x) = x \).

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