Find the Inverse -1/(4x)

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 ${\displaystyle -\frac{1}{4y}=x}$ by ${\displaystyle 4y}$.

Simplify the left side.

Simplify the right side.

Rewrite the equation as ${\displaystyle 4xy=-1}$.

Divide each term in ${\displaystyle 4xy=-1}$ by ${\displaystyle 4x}$ and simplify.

Set up the composite result function.

Evaluate ${\displaystyle f^{-1}(-\frac{1}{4x})}$ by substituting in the value of ${\displaystyle f}$ into ${\displaystyle f^{-1}}$.

Cancel the common factor of ${\displaystyle 1}$ and ${\displaystyle -1}$.

Combine ${\displaystyle 4}$ and ${\displaystyle \frac{1}{4x}}$.

Reduce the expression ${\displaystyle \frac{4}{4x}}$ by cancelling the common factors.

Multiply the numerator by the reciprocal of the denominator.

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

Set up the composite result function.

Evaluate ${\displaystyle f(-\frac{1}{4x})}$ by substituting in the value of ${\displaystyle f^{-1}}$ into ${\displaystyle f}$.

Cancel the common factor of ${\displaystyle 1}$ and ${\displaystyle -1}$.

Combine ${\displaystyle 4}$ and ${\displaystyle \frac{1}{4x}}$.

Reduce the expression ${\displaystyle \frac{4}{4x}}$ by cancelling the common factors.

Multiply the numerator by the reciprocal of the denominator.

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