Find the Inverse 10/y=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 ${\displaystyle \frac{10}{y}=x}$ by ${\displaystyle y}$.

Simplify the left side.

Rewrite the equation as ${\displaystyle xy=10}$.

Divide each term in ${\displaystyle xy=10}$ by ${\displaystyle x}$ and simplify.

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

Find the LCD of the terms in the equation.

Multiply each term in ${\displaystyle \frac{10}{y}=x}$ by ${\displaystyle y}$ to eliminate the fractions.

Solve the equation.

To verify the inverse, check if ${\displaystyle f^{-1}\left(f\left(x\right)\right)=x}$ and ${\displaystyle f\left(f^{-1}\left(x\right)\right)=x}$.

Evaluate ${\displaystyle f^{-1}\left(f\left(x\right)\right)}$.

Evaluate ${\displaystyle f\left(f^{-1}\left(x\right)\right)}$.

Since ${\displaystyle f^{-1}\left(f\left(x\right)\right)=x}$ and ${\displaystyle f\left(f^{-1}\left(x\right)\right)=x}$, then ${\displaystyle f^{-1}\left(x\right)=\frac{10}{x}}$ is the inverse of ${\displaystyle f\left(x\right)=\frac{10}{x}}$.