Find the Inverse f^-1(x)=1/(f(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 ${\displaystyle \frac{1}{yx}=f}$ by ${\displaystyle yx}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle fyx=1}$.

Divide each term in ${\displaystyle fyx=1}$ by ${\displaystyle fx}$ and simplify.

Write ${\displaystyle f\left(f\right)=\frac{1}{fx}}$ as an equation.

Interchange the variables.

Solve for ${\displaystyle y}$.

Replace ${\displaystyle y}$ with ${\displaystyle f^{-1}\left(f\right)}$ to show the final answer.

Set up the composite result function.

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

Combine ${\displaystyle \frac{1}{fx}}$ and ${\displaystyle x}$.

Reduce the expression ${\displaystyle \frac{x}{fx}}$ by cancelling the common factors.

Multiply the numerator by the reciprocal of the denominator.

Multiply ${\displaystyle f}$ by ${\displaystyle 1}$.

Write ${\displaystyle f\left(f\right)=\frac{1}{fx}}$ as an equation.

Interchange the variables.

Solve for ${\displaystyle y}$.

Replace ${\displaystyle y}$ with ${\displaystyle f^{-1}\left(f\right)}$ to show the final answer.

Set up the composite result function.

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

Combine ${\displaystyle \frac{1}{fx}}$ and ${\displaystyle x}$.

Reduce the expression ${\displaystyle \frac{x}{fx}}$ by cancelling the common factors.

Multiply the numerator by the reciprocal of the denominator.

Multiply ${\displaystyle f}$ by ${\displaystyle 1}$.