Find the Inverse (-2x)/17

$\frac{- 2 x}{17}$

Interchange the variables.

$x = \frac{- 2 y}{17}$

Solve for $y$ .

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Rewrite the equation as $\frac{- 2 y}{17} = x$ .

$\frac{- 2 y}{17} = x$

Multiply both sides of the equation by $\frac{17}{- 2}$ .

$\frac{17}{- 2} \cdot \frac{- 2 y}{17} = \frac{17}{- 2} x$

Simplify both sides of the equation.

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Simplify $\frac{17}{- 2} \cdot \frac{- 2 y}{17}$ .

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Cancel the common factor of $17$ .

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Cancel the common factor.

$\frac{17}{- 2} \cdot \frac{- 2 y}{17} = \frac{17}{- 2} x$

Rewrite the expression.

$\frac{1}{- 2} \cdot (- 2 y) = \frac{17}{- 2} x$

Cancel the common factor of $2$ .

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Factor $2$ out of $- 2$ .

$\frac{1}{2 (- 1)} \cdot (- 2 y) = \frac{17}{- 2} x$

Factor $2$ out of $- 2 y$ .

$\frac{1}{2 (- 1)} \cdot (2 (- y)) = \frac{17}{- 2} x$

Cancel the common factor.

$\frac{1}{2 \cdot - 1} \cdot (2 (- y)) = \frac{17}{- 2} x$

Rewrite the expression.

$\frac{1}{- 1} \cdot (- y) = \frac{17}{- 2} x$

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

$- \frac{y}{- 1} = \frac{17}{- 2} x$

Simplify the expression.

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Move the negative one from the denominator of $\frac{y}{- 1}$ .

$- (- 1 \cdot y) = \frac{17}{- 2} x$

Rewrite $- 1 \cdot y$ as $- y$ .

$- - y = \frac{17}{- 2} x$

Multiply $- - y$ .

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Multiply $- 1$ by $- 1$ .

$1 y = \frac{17}{- 2} x$

Multiply $y$ by $1$ .

$y = \frac{17}{- 2} x$

Simplify $\frac{17}{- 2} x$ .

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Move the negative in front of the fraction.

$y = - \frac{17}{2} x$

Combine $x$ and $\frac{17}{2}$ .

$y = - \frac{x \cdot 17}{2}$

Move $17$ to the left of $x$ .

$y = - \frac{17 x}{2}$

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.

$f^{- 1} (x) = - \frac{17 x}{2}$

Set up the composite result function.

$g (f (x))$

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

$g (\frac{- 2 x}{17}) = - \frac{17 (\frac{- 2 x}{17})}{2}$

Combine $17$ and $\frac{- 2 x}{17}$ .

$g (\frac{- 2 x}{17}) = - \frac{\frac{17 (- 2 x)}{17}}{2}$

Multiply $17$ by $- 2$ .

$g (\frac{- 2 x}{17}) = - \frac{\frac{- 34 x}{17}}{2}$

Reduce the expression by cancelling the common factors.

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Reduce the expression $\frac{- 34 x}{17}$ by cancelling the common factors.

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Factor $17$ out of $- 34 x$ .

$g (\frac{- 2 x}{17}) = - \frac{\frac{17 (- 2 x)}{17}}{2}$

Factor $17$ out of $17$ .

$g (\frac{- 2 x}{17}) = - \frac{\frac{17 (- 2 x)}{17 (1)}}{2}$

Cancel the common factor.

$g (\frac{- 2 x}{17}) = - \frac{\frac{17 (- 2 x)}{17 \cdot 1}}{2}$

Rewrite the expression.

$g (\frac{- 2 x}{17}) = - \frac{\frac{- 2 x}{1}}{2}$

Divide $- 2 x$ by $1$ .

$g (\frac{- 2 x}{17}) = - \frac{- 2 x}{2}$

Cancel the common factor of $- 2$ and $2$ .

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Factor $2$ out of $- 2 x$ .

$g (\frac{- 2 x}{17}) = - \frac{2 (- x)}{2}$

Cancel the common factors.

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Factor $2$ out of $2$ .

$g (\frac{- 2 x}{17}) = - \frac{2 (- x)}{2 (1)}$

Cancel the common factor.

$g (\frac{- 2 x}{17}) = - \frac{2 (- x)}{2 \cdot 1}$

Rewrite the expression.

$g (\frac{- 2 x}{17}) = - \frac{- x}{1}$

Divide $- x$ by $1$ .

$g (\frac{- 2 x}{17}) = x$

Since $g (f (x)) = x$ , $f^{- 1} (x) = - \frac{17 x}{2}$ is the inverse of $f (x) = \frac{- 2 x}{17}$ .

$f^{- 1} (x) = - \frac{17 x}{2}$

Find the Inverse (-2x)/17

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