Finite Math Examples

$f (x) = m$

Step 1

Write $f (x) = m$ as an equation.

$y = m$

Step 2

Interchange the variables.

$m = y$

Step 3

Rewrite the equation as $y = m$ .

$y = m$

Step 4

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

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

Step 5

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

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Step 5.1

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

Step 5.2

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

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Step 5.2.1

Set up the composite result function.

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

Step 5.2.2

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

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

Step 5.2.3

Remove parentheses.

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

Step 5.3

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

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Step 5.3.1

Set up the composite result function.

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

Step 5.3.2

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

$f (m) = m$

Step 5.3.3

Remove parentheses.

$f (m) = m$

Step 5.4

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

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