Finite Math Examples

$- a$

Step 1

Interchange the variables.

$a = - y$

Step 2

Solve for $y$ .

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Step 2.1

Rewrite the equation as $- y = a$ .

$- y = a$

Step 2.2

Divide each term in $- y = a$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- y = a$ by $- 1$ .

$\frac{- y}{- 1} = \frac{a}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{a}{- 1}$

Step 2.2.2.2

Divide $y$ by $1$ .

$y = \frac{a}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Move the negative one from the denominator of $\frac{a}{- 1}$ .

$y = - 1 \cdot a$

Step 2.2.3.2

Rewrite $- 1 \cdot a$ as $- a$ .

$y = - a$

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

Multiply $- (- a)$ .

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Step 4.2.3.1

Multiply $- 1$ by $- 1$ .

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

Step 4.2.3.2

Multiply $a$ by $1$ .

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

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

Multiply $- (- a)$ .

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Step 4.3.3.1

Multiply $- 1$ by $- 1$ .

$f (- a) = 1 a$

Step 4.3.3.2

Multiply $a$ by $1$ .

$f (- a) = a$

Step 4.4

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

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