Find the Inverse (x-5)/6

$\frac{x - 5}{6}$

Step 1

Interchange the variables.

$x = \frac{y - 5}{6}$

Step 2

Solve for $y$ .

Rewrite the equation as $\frac{y - 5}{6} = x$ .

$\frac{y - 5}{6} = x$

Multiply both sides of the equation by $6$ .

$6 \frac{y - 5}{6} = 6 x$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$6 \frac{y - 5}{6} = 6 x$

Rewrite the expression.

$y - 5 = 6 x$

Add $5$ to both sides of the equation.

$y = 6 x + 5$

Step 3

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

$f^{- 1} (x) = 6 x + 5$

Step 4

Verify if $f^{- 1} (x) = 6 x + 5$ is the inverse of $f (x) = \frac{x - 5}{6}$ .

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 $f^{- 1} (\frac{x - 5}{6})$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} (\frac{x - 5}{6}) = 6 (\frac{x - 5}{6}) + 5$

Cancel the common factor of $6$ .

Cancel the common factor.

$f^{- 1} (\frac{x - 5}{6}) = 6 (\frac{x - 5}{6}) + 5$

Rewrite the expression.

$f^{- 1} (\frac{x - 5}{6}) = x - 5 + 5$

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

Add $- 5$ and $5$ .

$f^{- 1} (\frac{x - 5}{6}) = x + 0$

Add $x$ and $0$ .

$f^{- 1} (\frac{x - 5}{6}) = x$

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

Set up the composite result function.

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

Evaluate $f (6 x + 5)$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (6 x + 5) = \frac{(6 x + 5) - 5}{6}$

Simplify the numerator.

Subtract $5$ from $5$ .

$f (6 x + 5) = \frac{6 x + 0}{6}$

Add $6 x$ and $0$ .

$f (6 x + 5) = \frac{6 x}{6}$

Cancel the common factor of $6$ .

Cancel the common factor.

$f (6 x + 5) = \frac{6 x}{6}$

Divide $x$ by $1$ .

$f (6 x + 5) = x$

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = 6 x + 5$ is the inverse of $f (x) = \frac{x - 5}{6}$ .

$f^{- 1} (x) = 6 x + 5$

Find the Inverse (x-5)/6

Related Questions

Support LCMGCF.com by disabling your adblocker.