Find the Inverse m(x)=(x+5)/2

$m (x) = \frac{x + 5}{2}$

Step 1

Write $m (x) = \frac{x + 5}{2}$ as an equation.

$y = \frac{x + 5}{2}$

Step 2

Interchange the variables.

$x = \frac{y + 5}{2}$

Step 3

Solve for $y$ .

Rewrite the equation as $\frac{y + 5}{2} = x$ .

$\frac{y + 5}{2} = x$

Multiply both sides of the equation by $2$ .

$2 \frac{y + 5}{2} = 2 x$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{y + 5}{2} = 2 x$

Rewrite the expression.

$y + 5 = 2 x$

Subtract $5$ from both sides of the equation.

$y = 2 x - 5$

Step 4

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

$m^{- 1} (x) = 2 x - 5$

Step 5

Verify if $m^{- 1} (x) = 2 x - 5$ is the inverse of $m (x) = \frac{x + 5}{2}$ .

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

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

Set up the composite result function.

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

Evaluate $m^{- 1} (\frac{x + 5}{2})$ by substituting in the value of $m$ into $m^{- 1}$ .

$m^{- 1} (\frac{x + 5}{2}) = 2 (\frac{x + 5}{2}) - 5$

Cancel the common factor of $2$ .

Cancel the common factor.

$m^{- 1} (\frac{x + 5}{2}) = 2 (\frac{x + 5}{2}) - 5$

Rewrite the expression.

$m^{- 1} (\frac{x + 5}{2}) = x + 5 - 5$

Combine the opposite terms in $x + 5 - 5$ .

Subtract $5$ from $5$ .

$m^{- 1} (\frac{x + 5}{2}) = x + 0$

Add $x$ and $0$ .

$m^{- 1} (\frac{x + 5}{2}) = x$

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

Set up the composite result function.

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

Evaluate $m (2 x - 5)$ by substituting in the value of $m^{- 1}$ into $m$ .

$m (2 x - 5) = \frac{(2 x - 5) + 5}{2}$

Simplify the numerator.

Add $- 5$ and $5$ .

$m (2 x - 5) = \frac{2 x + 0}{2}$

Add $2 x$ and $0$ .

$m (2 x - 5) = \frac{2 x}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$m (2 x - 5) = \frac{2 x}{2}$

Divide $x$ by $1$ .

$m (2 x - 5) = x$

Since $m^{- 1} (m (x)) = x$ and $m (m^{- 1} (x)) = x$ , then $m^{- 1} (x) = 2 x - 5$ is the inverse of $m (x) = \frac{x + 5}{2}$ .

$m^{- 1} (x) = 2 x - 5$

Find the Inverse m(x)=(x+5)/2

Related Questions

Support LCMGCF.com by disabling your adblocker.