To solve for x, compute the inverse function f⁻¹ and apply it to both sides of the equation.

An inversion pair of a permutation σ is a pair of indices (i, j) with i < j and σ(i) > σ(j), and counting all such inversion pairs yields the inversion number.

To find the original angle from its cosine, she used the inverse cosine to calculate the measure.

In classical inversive geometry, a circle inversion with center O and radius r maps any point P ≠ O to the point P' on the ray from O through P for which OP × OP' = r², and maps O to the point at infinity.

The researchers proved that the inverse semigroup formed by the partial bijections of the set fully characterizes the system's local symmetries.

In many papers, inverse semigroups are used to model partial symmetries in operator algebras.

Recent research in inversive geometry has revealed unexpected connections between circle inversions and modern conformal field theories.

Students learned that additive inverses always cancel each other when added.

The composer used a retrograde inversion to turn the inversion of the tone row backward, creating a darker mirror of the original series.

Philosophers often analyze conceptual inverses to clarify how opposing ideas shape each other's meanings.