Find the Inverse x/12+15

$\frac{x}{12} + 15$

Step 1

Interchange the variables.

$x = \frac{y}{12} + 15$

Step 2

Solve for $y$ .

Rewrite the equation as $\frac{y}{12} + 15 = x$ .

$\frac{y}{12} + 15 = x$

Subtract $15$ from both sides of the equation.

$\frac{y}{12} = x - 15$

Multiply both sides of the equation by $12$ .

$12 \frac{y}{12} = 12 (x - 15)$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$12 \frac{y}{12} = 12 (x - 15)$

Rewrite the expression.

$y = 12 (x - 15)$

Simplify the right side.

Simplify $12 (x - 15)$ .

Apply the distributive property.

$y = 12 x + 12 \cdot - 15$

Multiply $12$ by $- 15$ .

$y = 12 x - 180$

Step 3

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

$f^{- 1} (x) = 12 x - 180$

Step 4

Verify if $f^{- 1} (x) = 12 x - 180$ is the inverse of $f (x) = \frac{x}{12} + 15$ .

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 $f^{- 1} (\frac{x}{12} + 15)$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} (\frac{x}{12} + 15) = 12 (\frac{x}{12} + 15) - 180$

Simplify each term.

Apply the distributive property.

$f^{- 1} (\frac{x}{12} + 15) = 12 (\frac{x}{12}) + 12 \cdot 15 - 180$

Cancel the common factor of $12$ .

Cancel the common factor.

$f^{- 1} (\frac{x}{12} + 15) = 12 (\frac{x}{12}) + 12 \cdot 15 - 180$

Rewrite the expression.

$f^{- 1} (\frac{x}{12} + 15) = x + 12 \cdot 15 - 180$

Multiply $12$ by $15$ .

$f^{- 1} (\frac{x}{12} + 15) = x + 180 - 180$

Combine the opposite terms in $x + 180 - 180$ .

Subtract $180$ from $180$ .

$f^{- 1} (\frac{x}{12} + 15) = x + 0$

Add $x$ and $0$ .

$f^{- 1} (\frac{x}{12} + 15) = x$

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

Set up the composite result function.

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

Evaluate $f (12 x - 180)$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (12 x - 180) = \frac{12 x - 180}{12} + 15$

Cancel the common factor of $12 x - 180$ and $12$ .

Factor $12$ out of $12 x$ .

$f (12 x - 180) = \frac{12 (x) - 180}{12} + 15$

Factor $12$ out of $- 180$ .

$f (12 x - 180) = \frac{12 (x) + 12 \cdot - 15}{12} + 15$

Factor $12$ out of $12 (x) + 12 (- 15)$ .

$f (12 x - 180) = \frac{12 (x - 15)}{12} + 15$

Cancel the common factors.

Factor $12$ out of $12$ .

$f (12 x - 180) = \frac{12 (x - 15)}{12 (1)} + 15$

Cancel the common factor.

$f (12 x - 180) = \frac{12 (x - 15)}{12 \cdot 1} + 15$

Rewrite the expression.

$f (12 x - 180) = \frac{x - 15}{1} + 15$

Divide $x - 15$ by $1$ .

$f (12 x - 180) = x - 15 + 15$

Combine the opposite terms in $x - 15 + 15$ .

Add $- 15$ and $15$ .

$f (12 x - 180) = x + 0$

Add $x$ and $0$ .

$f (12 x - 180) = x$

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = 12 x - 180$ is the inverse of $f (x) = \frac{x}{12} + 15$ .

$f^{- 1} (x) = 12 x - 180$

Find the Inverse x/12+15

Related Questions

Support LCMGCF.com by disabling your adblocker.