Find the Inverse 1/9x+2

$\frac{1}{9} x + 2$

Interchange the variables.

$x = \frac{1}{9} y + 2$

Solve for $y$ .

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Rewrite the equation as $\frac{1}{9} y + 2 = x$ .

$\frac{1}{9} y + 2 = x$

Combine $\frac{1}{9}$ and $y$ .

$\frac{y}{9} + 2 = x$

Subtract $2$ from both sides of the equation.

$\frac{y}{9} = x - 2$

Multiply both sides of the equation by $9$ .

$9 \cdot \frac{y}{9} = 9 \cdot (x - 2)$

Simplify both sides of the equation.

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Cancel the common factor of $9$ .

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Cancel the common factor.

$9 \cdot \frac{y}{9} = 9 \cdot (x - 2)$

Rewrite the expression.

$y = 9 \cdot (x - 2)$

Simplify $9 \cdot (x - 2)$ .

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Apply the distributive property.

$y = 9 x + 9 \cdot - 2$

Multiply $9$ by $- 2$ .

$y = 9 x - 18$

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.

$f^{- 1} (x) = 9 x - 18$

Set up the composite result function.

$g (f (x))$

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

$g (\frac{1}{9} x + 2) = 9 (\frac{1}{9} x + 2) - 18$

Simplify each term.

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Combine $\frac{1}{9}$ and $x$ .

$g (\frac{1}{9} x + 2) = 9 (\frac{x}{9} + 2) - 18$

Apply the distributive property.

$g (\frac{1}{9} x + 2) = 9 (\frac{x}{9}) + 9 \cdot 2 - 18$

Cancel the common factor of $9$ .

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Cancel the common factor.

$g (\frac{1}{9} x + 2) = 9 (\frac{x}{9}) + 9 \cdot 2 - 18$

Rewrite the expression.

$g (\frac{1}{9} x + 2) = x + 9 \cdot 2 - 18$

Multiply $9$ by $2$ .

$g (\frac{1}{9} x + 2) = x + 18 - 18$

Combine the opposite terms in $x + 18 - 18$ .

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Subtract $18$ from $18$ .

$g (\frac{1}{9} x + 2) = x + 0$

Add $x$ and $0$ .

$g (\frac{1}{9} x + 2) = x$

Since $g (f (x)) = x$ , $f^{- 1} (x) = 9 x - 18$ is the inverse of $f (x) = \frac{1}{9} x + 2$ .

$f^{- 1} (x) = 9 x - 18$

Find the Inverse 1/9x+2

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