Find the Inverse f(x)=1/6x

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

Write $f (x) = \frac{1}{6} x$ as an equation.

$y = \frac{1}{6} x$

Interchange the variables.

$x = \frac{1}{6} y$

Solve for $y$ .

Rewrite the equation as $\frac{1}{6} y = x$ .

$\frac{1}{6} y = x$

Multiply both sides of the equation by $6$ .

$6 (\frac{1}{6} y) = 6 x$

Simplify the left side.

Simplify $6 (\frac{1}{6} y)$ .

Combine $\frac{1}{6}$ and $y$ .

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

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

$y = 6 x$

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

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

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

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

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

Combine $\frac{1}{6}$ and $x$ .

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

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Set up the composite result function.

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

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

$f (6 x) = \frac{1}{6} \cdot (6 x)$

Cancel the common factor of $6$ .

Factor $6$ out of $6 x$ .

$f (6 x) = \frac{1}{6} \cdot (6 (x))$

Cancel the common factor.

$f (6 x) = \frac{1}{6} \cdot (6 x)$

Rewrite the expression.

$f (6 x) = x$

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

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

Find the Inverse f(x)=1/6x

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