Find the Inverse 15x+30

$15 x + 30$

Step 1

Interchange the variables.

$x = 15 y + 30$

Step 2

Solve for $y$ .

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

$15 y + 30 = x$

Subtract $30$ from both sides of the equation.

$15 y = x - 30$

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

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

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

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Divide $- 30$ by $15$ .

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

Step 3

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

$f^{- 1} (x) = \frac{x}{15} - 2$

Step 4

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

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

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

Set up the composite result function.

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

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

$f^{- 1} (15 x + 30) = \frac{15 x + 30}{15} - 2$

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

Factor $15$ out of $15 x$ .

$f^{- 1} (15 x + 30) = \frac{15 (x) + 30}{15} - 2$

Factor $15$ out of $30$ .

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

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

$f^{- 1} (15 x + 30) = \frac{15 (x + 2)}{15} - 2$

Cancel the common factors.

Factor $15$ out of $15$ .

$f^{- 1} (15 x + 30) = \frac{15 (x + 2)}{15 (1)} - 2$

Cancel the common factor.

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

Rewrite the expression.

$f^{- 1} (15 x + 30) = \frac{x + 2}{1} - 2$

Divide $x + 2$ by $1$ .

$f^{- 1} (15 x + 30) = x + 2 - 2$

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

Subtract $2$ from $2$ .

$f^{- 1} (15 x + 30) = x + 0$

Add $x$ and $0$ .

$f^{- 1} (15 x + 30) = x$

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

Set up the composite result function.

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

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

$f (\frac{x}{15} - 2) = 15 (\frac{x}{15} - 2) + 30$

Simplify each term.

Apply the distributive property.

$f (\frac{x}{15} - 2) = 15 (\frac{x}{15}) + 15 \cdot - 2 + 30$

Cancel the common factor of $15$ .

Cancel the common factor.

$f (\frac{x}{15} - 2) = 15 (\frac{x}{15}) + 15 \cdot - 2 + 30$

Rewrite the expression.

$f (\frac{x}{15} - 2) = x + 15 \cdot - 2 + 30$

Multiply $15$ by $- 2$ .

$f (\frac{x}{15} - 2) = x - 30 + 30$

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

Add $- 30$ and $30$ .

$f (\frac{x}{15} - 2) = x + 0$

Add $x$ and $0$ .

$f (\frac{x}{15} - 2) = x$

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

$f^{- 1} (x) = \frac{x}{15} - 2$

Find the Inverse 15x+30

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