---
title: "Inverse superscript mathematical notation"
description: "The superscript negative one can denote a reciprocal, matrix inverse, inverse function, or set preimage depending on the base object's type."
canonical_url: "https://fanout.sh/labs/math-decoder/symbol/inverse-superscript"
md_url: "https://fanout.sh/labs/math-decoder/symbol/inverse-superscript.md"
last_updated: "2026-08-09"
access: "public"
---

# Inverse superscript mathematical notation

The superscript negative one can denote a reciprocal, matrix inverse, inverse function, or set preimage depending on the base object's type.

## Public overview

Scalar reciprocal: For a nonzero scalar, returns the multiplicative reciprocal that produces one when multiplied by the base. Example: The reciprocal of nonzero x multiplies with x to make one.

Matrix inverse: For an invertible square matrix, returns the matrix that composes with it to produce the identity. Example: The inverse undoes the matrix transformation.

Inverse function: For a bijective function, reverses the mapping so outputs return to their unique inputs. Example: Applying the inverse after f recovers the original input.

Set preimage: Returns all domain elements whose function outputs fall inside a specified set, without requiring invertibility. Example: Collect every input that f sends into set S.

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