Find the Inverse C(n)=15n+30

$C (n) = 15 n + 30$

Step 1

Write $C (n) = 15 n + 30$ as an equation.

$y = 15 n + 30$

Step 2

Interchange the variables.

$n = 15 y + 30$

Step 3

Solve for $y$ .

Rewrite the equation as $15 y + 30 = n$ .

$15 y + 30 = n$

Subtract $30$ from both sides of the equation.

$15 y = n - 30$

Divide each term in $15 y = n - 30$ by $15$ and simplify.

Divide each term in $15 y = n - 30$ by $15$ .

$\frac{15 y}{15} = \frac{n}{15} + \frac{- 30}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 y}{15} = \frac{n}{15} + \frac{- 30}{15}$

Divide $y$ by $1$ .

$y = \frac{n}{15} + \frac{- 30}{15}$

Simplify the right side.

Divide $- 30$ by $15$ .

$y = \frac{n}{15} - 2$

Step 4

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

$C^{- 1} (n) = \frac{n}{15} - 2$

Step 5

Verify if $C^{- 1} (n) = \frac{n}{15} - 2$ is the inverse of $C (n) = 15 n + 30$ .

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

Evaluate $C^{- 1} (C (n))$ .

Set up the composite result function.

$C^{- 1} (C (n))$

Evaluate $C^{- 1} (15 n + 30)$ by substituting in the value of $C$ into $C^{- 1}$ .

$C^{- 1} (15 n + 30) = \frac{15 n + 30}{15} - 2$

Cancel the common factor of $15 n + 30$ and $15$ .

Factor $15$ out of $15 n$ .

$C^{- 1} (15 n + 30) = \frac{15 (n) + 30}{15} - 2$

Factor $15$ out of $30$ .

$C^{- 1} (15 n + 30) = \frac{15 (n) + 15 \cdot 2}{15} - 2$

Factor $15$ out of $15 (n) + 15 (2)$ .

$C^{- 1} (15 n + 30) = \frac{15 (n + 2)}{15} - 2$

Cancel the common factors.

Factor $15$ out of $15$ .

$C^{- 1} (15 n + 30) = \frac{15 (n + 2)}{15 (1)} - 2$

Cancel the common factor.

$C^{- 1} (15 n + 30) = \frac{15 (n + 2)}{15 \cdot 1} - 2$

Rewrite the expression.

$C^{- 1} (15 n + 30) = \frac{n + 2}{1} - 2$

Divide $n + 2$ by $1$ .

$C^{- 1} (15 n + 30) = n + 2 - 2$

Combine the opposite terms in $n + 2 - 2$ .

Subtract $2$ from $2$ .

$C^{- 1} (15 n + 30) = n + 0$

Add $n$ and $0$ .

$C^{- 1} (15 n + 30) = n$

Evaluate $C (C^{- 1} (n))$ .

Set up the composite result function.

$C (C^{- 1} (n))$

Evaluate $C (\frac{n}{15} - 2)$ by substituting in the value of $C^{- 1}$ into $C$ .

$C (\frac{n}{15} - 2) = 15 (\frac{n}{15} - 2) + 30$

Simplify each term.

Apply the distributive property.

$C (\frac{n}{15} - 2) = 15 (\frac{n}{15}) + 15 \cdot - 2 + 30$

Cancel the common factor of $15$ .

Cancel the common factor.

$C (\frac{n}{15} - 2) = 15 (\frac{n}{15}) + 15 \cdot - 2 + 30$

Rewrite the expression.

$C (\frac{n}{15} - 2) = n + 15 \cdot - 2 + 30$

Multiply $15$ by $- 2$ .

$C (\frac{n}{15} - 2) = n - 30 + 30$

Combine the opposite terms in $n - 30 + 30$ .

Add $- 30$ and $30$ .

$C (\frac{n}{15} - 2) = n + 0$

Add $n$ and $0$ .

$C (\frac{n}{15} - 2) = n$

Since $C^{- 1} (C (n)) = n$ and $C (C^{- 1} (n)) = n$ , then $C^{- 1} (n) = \frac{n}{15} - 2$ is the inverse of $C (n) = 15 n + 30$ .

$C^{- 1} (n) = \frac{n}{15} - 2$

Find the Inverse C(n)=15n+30

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