Find the Inverse (x-5)/6

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

Interchange the variables.

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

Solve for $y$ .

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

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

Multiply both sides of the equation by $6$ .

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

Cancel the common factor of $6$ .

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Cancel the common factor.

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

Rewrite the expression.

$y - 5 = 6 \cdot x$

$y - 5 = 6 x$

Add $5$ to both sides of the equation.

$y = 6 x + 5$

Solve for $y$ and replace with $f^{- 1} (x)$ .

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

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

Set up the composite result function.

$g (f (x))$

Evaluate $g (f (x))$ by substituting in the value of $f$ into $g$ .

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

Cancel the common factor of $6$ .

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Cancel the common factor.

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

Rewrite the expression.

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

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

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Add $- 5$ and $5$ .

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

Add $x$ and $0$ .

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

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

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

Find the Inverse (x-5)/6

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