Find the Inverse 10/x

$\frac{10}{x}$

Interchange the variables.

$x = \frac{10}{y}$

Solve for $y$ .

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Rewrite the equation as $\frac{10}{y} = x$ .

$\frac{10}{y} = x$

Solve for $y$ .

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Multiply each term by $y$ and simplify.

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Multiply each term in $\frac{10}{y} = x$ by $y$ .

$\frac{10}{y} \cdot y = x \cdot y$

Cancel the common factor of $y$ .

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Cancel the common factor.

$\frac{10}{y} \cdot y = x \cdot y$

Rewrite the expression.

$10 = x \cdot y$

$10 = x y$

Rewrite the equation as $x y = 10$ .

$x y = 10$

Divide each term by $x$ and simplify.

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Divide each term in $x y = 10$ by $x$ .

$\frac{x y}{x} = \frac{10}{x}$

Cancel the common factor of $x$ .

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Cancel the common factor.

$\frac{x y}{x} = \frac{10}{x}$

Divide $y$ by $1$ .

$y = \frac{10}{x}$

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.

$f^{- 1} (x) = \frac{10}{x}$

Set up the composite result function.

$g (f (x))$

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

$g (\frac{10}{x}) = \frac{10}{\frac{10}{x}}$

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{10}{x}) = 10 (\frac{x}{10})$

Cancel the common factor of $10$ .

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Cancel the common factor.

$g (\frac{10}{x}) = 10 (\frac{x}{10})$

Rewrite the expression.

$g (\frac{10}{x}) = x$

Since $g (f (x)) = x$ , $f^{- 1} (x) = \frac{10}{x}$ is the inverse of $f (x) = \frac{10}{x}$ .

$f^{- 1} (x) = \frac{10}{x}$

Find the Inverse 10/x

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