Finite Math Examples

$a$

Step 1

Interchange the variables.

$a = y$

Step 2

Rewrite the equation as $y = a$ .

$y = a$

Step 3

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

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

Step 4

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

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Step 4.1

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

Step 4.2

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

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Step 4.2.1

Set up the composite result function.

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

Step 4.2.2

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

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

Step 4.2.3

Remove parentheses.

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

Step 4.3

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

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Step 4.3.1

Set up the composite result function.

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

Step 4.3.2

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

$f (a) = a$

Step 4.3.3

Remove parentheses.

$f (a) = a$

Step 4.4

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

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