Finite Math Examples

$F (x) = x$

Step 1

Write $F (x) = x$ as an equation.

$y = x$

Step 2

Interchange the variables.

$x = y$

Step 3

Rewrite the equation as $y = x$ .

$y = x$

Step 4

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

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

Step 5

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

Tap for more steps...

Step 5.1

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

Step 5.2

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

Tap for more steps...

Step 5.2.1

Set up the composite result function.

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

Step 5.2.2

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

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

Step 5.2.3

Remove parentheses.

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

Step 5.3

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

Tap for more steps...

Step 5.3.1

Set up the composite result function.

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

Step 5.3.2

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

$F (x) = x$

Step 5.3.3

Remove parentheses.

$F (x) = x$

Step 5.4

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

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