Find the Inverse -5x-11

$- 5 x - 11$

Interchange the variables.

$x = - 5 y - 11$

Solve for $y$ .

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Rewrite the equation as $- 5 y - 11 = x$ .

$- 5 y - 11 = x$

Add $11$ to both sides of the equation.

$- 5 y = x + 11$

Divide each term by $- 5$ and simplify.

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Divide each term in $- 5 y = x + 11$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{x}{- 5} + \frac{11}{- 5}$

Cancel the common factor of $- 5$ .

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Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{x}{- 5} + \frac{11}{- 5}$

Divide $y$ by $1$ .

$y = \frac{x}{- 5} + \frac{11}{- 5}$

Simplify each term.

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Move the negative in front of the fraction.

$y = - \frac{x}{5} + \frac{11}{- 5}$

Move the negative in front of the fraction.

$y = - \frac{x}{5} - \frac{11}{5}$

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.

$f^{- 1} (x) = - \frac{x}{5} - \frac{11}{5}$

Set up the composite result function.

$g (f (x))$

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

$g (- 5 x - 11) = - \frac{- 5 x - 11}{5} - \frac{11}{5}$

Combine the numerators over the common denominator.

$g (- 5 x - 11) = \frac{- (- 5 x - 11) - 11}{5}$

Simplify the numerator.

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Factor $- 1$ out of $- (- 5 x - 11) - 11$ .

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Rewrite $- 11$ as $- 1 (11)$ .

$g (- 5 x - 11) = \frac{- (- 5 x - 11) - 1 \cdot 11}{5}$

Factor $- 1$ out of $- (- 5 x - 11) - 1 (11)$ .

$g (- 5 x - 11) = \frac{- (- 5 x - 11 + 11)}{5}$

Add $- 11$ and $11$ .

$g (- 5 x - 11) = \frac{- (- 5 x + 0)}{5}$

Add $- 5 x$ and $0$ .

$g (- 5 x - 11) = \frac{5 x}{5}$

Multiply $- 1$ by $- 5$ .

$g (- 5 x - 11) = \frac{5 x}{5}$

Cancel the common factor of $5$ .

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Cancel the common factor.

$g (- 5 x - 11) = \frac{5 x}{5}$

Divide $x$ by $1$ .

$g (- 5 x - 11) = x$

Since $g (f (x)) = x$ , $f^{- 1} (x) = - \frac{x}{5} - \frac{11}{5}$ is the inverse of $f (x) = - 5 x - 11$ .

$f^{- 1} (x) = - \frac{x}{5} - \frac{11}{5}$

Find the Inverse -5x-11

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