Find the Inverse 20x

$20 x$

Step 1

Interchange the variables.

$x = 20 y$

Step 2

Solve for $y$ .

Rewrite the equation as $20 y = x$ .

$20 y = x$

Divide each term in $20 y = x$ by $20$ and simplify.

Divide each term in $20 y = x$ by $20$ .

$\frac{20 y}{20} = \frac{x}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 y}{20} = \frac{x}{20}$

Divide $y$ by $1$ .

$y = \frac{x}{20}$

Step 3

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

$f^{- 1} (x) = \frac{x}{20}$

Step 4

Verify if $f^{- 1} (x) = \frac{x}{20}$ is the inverse of $f (x) = 20 x$ .

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 $f^{- 1} (20 x)$ by substituting in the value of $f$ into $f^{- 1}$ .

$f^{- 1} (20 x) = \frac{20 x}{20}$

Cancel the common factor of $20$ .

Cancel the common factor.

$f^{- 1} (20 x) = \frac{20 x}{20}$

Divide $x$ by $1$ .

$f^{- 1} (20 x) = x$

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

Set up the composite result function.

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

Evaluate $f (\frac{x}{20})$ by substituting in the value of $f^{- 1}$ into $f$ .

$f (\frac{x}{20}) = 20 (\frac{x}{20})$

Cancel the common factor of $20$ .

Cancel the common factor.

$f (\frac{x}{20}) = 20 (\frac{x}{20})$

Rewrite the expression.

$f (\frac{x}{20}) = x$

Since $f^{- 1} (f (x)) = x$ and $f (f^{- 1} (x)) = x$ , then $f^{- 1} (x) = \frac{x}{20}$ is the inverse of $f (x) = 20 x$ .

$f^{- 1} (x) = \frac{x}{20}$