Find the Inverse g(x)=5x

$g (x) = 5 x$

Step 1

Write $g (x) = 5 x$ as an equation.

$y = 5 x$

Step 2

Interchange the variables.

$x = 5 y$

Step 3

Solve for $y$ .

Rewrite the equation as $5 y = x$ .

$5 y = x$

Divide each term in $5 y = x$ by $5$ and simplify.

Divide each term in $5 y = x$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Step 4

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

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

Step 5

Verify if $g^{- 1} (x) = \frac{x}{5}$ is the inverse of $g (x) = 5 x$ .

To verify the inverse, check if $g^{- 1} (g (x)) = x$ and $g (g^{- 1} (x)) = x$ .

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

Set up the composite result function.

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

Evaluate $g^{- 1} (5 x)$ by substituting in the value of $g$ into $g^{- 1}$ .

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

$g^{- 1} (5 x) = x$

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

Set up the composite result function.

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

Evaluate $g (\frac{x}{5})$ by substituting in the value of $g^{- 1}$ into $g$ .

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

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Find the Inverse g(x)=5x

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