Find the Inverse y=x

$y = x$

Step 1

Interchange the variables.

$x = y$

Step 2

Rewrite the equation as $y = x$ .

$y = x$

Step 3

Replace $y$ with $f^{- 1} (x)$ to show the final answer.

$f^{- 1} (x) = x$

Step 4

Verify if $f^{- 1} (x) = x$ is the inverse of $f (x) = x$ .

To verify the inverse, check if $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ .

Evaluate $f^{- 1} (f (x))$ .

Set up the composite result function.

$f^{- 1} (f (x))$

Evaluate $f^{- 1} (x)$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} (x) = x$

Remove parentheses.

$f^{- 1} (x) = x$

Evaluate $f (f^{- 1} (x))$ .

Set up the composite result function.

$f (f^{- 1} (x))$

Evaluate $f (x)$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (x) = x$

Remove parentheses.

$f (x) = x$

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = x$ is the inverse of $f (x) = x$ .

$f^{- 1} (x) = x$