Find the Inverse 9/x

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

The LCM of one and any expression is the expression.

Multiply each term in ${\displaystyle \frac{9}{y}=x}$ by ${\displaystyle y}$.

Simplify the left side.

Rewrite the equation as ${\displaystyle xy=9}$.

Divide each term in ${\displaystyle xy=9}$ by ${\displaystyle x}$ and simplify.

Set up the composite result function.

Evaluate ${\displaystyle f^{-1}\left(\frac{9}{x}\right)}$ by substituting in the value of ${\displaystyle f}$ into ${\displaystyle f^{-1}}$.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of ${\displaystyle 9}$.

Set up the composite result function.

Evaluate ${\displaystyle f\left(\frac{9}{x}\right)}$ by substituting in the value of ${\displaystyle f^{-1}}$ into ${\displaystyle f}$.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of ${\displaystyle 9}$.