IN MATH: 1. n. an operation or function which UNDOES another operation or function . EX. Addition of 5 undoes subtraction of 5.
 OPERATION ITS INVERSE adding subtracting subtracting adding multiplying dividing multiplying factoring squaring square-rooting raising to the second power raising to the 1/2 power taking the opposite taking the opposite taking the reciprocal taking the reciprocal

2. n. for addition & subtraction, functions with identities, each operation, each number has its own inverse. For an operation with an identity (For the operation addition, the identity is 0. For the operation of multiplication, the identity is 1.), one number of a pair of numbers, whose operation together results in the identity
• for addition, its called the opposite;
• for multiplication, its called the reciprocal;

• FOR EXAMPLE:
```     number, operation, inverse, =, identity
5       +         -5    =  0
-5       +         5    =  0
5      times      1/5   is 1
1/5     times      5   is 1```
 function & inverse
 f(x), function f-1(x), inverse function x, do nothing x, do nothing -x, take opposite -x, take opposite 1/x, or x-1, take reciprocal 1/x, or x-1, take reciprocal x², square x or x1/2, square root x, or x1/2, square root x2, square x3, cube x1/3, cube root sin(x), take the sine sin-1(x)take the Arcsine sin-1(x)take the Arcsine sin(x) take the sine cos(x), take the cosine cos-1(x), take the Arccosine cos-1(x), take the Arccosine cos(x), take the cosine tan(x), take the tangent tan-1(x) take the Arctangent tan-1(x), take the Arctangent tan(x), take the tangent ... secant, cosecant, cotangent ... Arcsecant, Arccosecant, Arccotangent log(x), take the common log 10x, raise 10 to that power 10x, raise 10 to a power log(x) take the common log ln(x), take the natural log ex, raise e to that power ex, raise e to a power ln(x), take the natural log bx, raise b to a power logb(x), take a log with that base logb(x), take a log with a certain base bx, raise that base to a power Dx(y) or dy/dx, or f'(x), take a derivative f(x)dx, take an antiderivative f(x)dx, take an antiderivative Dx(y) or dy/dx, or f'(x), take a derivative limx cf(x), take a limit there is no inverse
 See Tools to Demonstrate Many Necessary Concepts: inverse.gsp - Geometer Sketchpad of inverse functions other videos inverse video See Arithmetic Stuff: inverse -- Inverse Math Spoken Here! dictionary definition problems pdf -- * 3 Problems & Answers set up to first take an inverse graphically then room for algebraically See Precalc Stuff: Inverse function notes -- Notes on Inverse Functions including taking in inerse function verbally inverse web page -- Find the Inverse of a Function in 4 Modalities Finding Angles & Sides Connect-the-Dots pdf -- Requires using arcfunctions to compute angle measures inverse function problems web page -- Problems & Answers on Finding Inverses Verbally, Graphically, Algebraically Arc and arc functions See Calc Stuff: m131Dinverse.pdf --- warm-Up on Notes on Taking the Derivative of an Inverse Trig Function, Arc Functions Derivatives of an Arc Functions - In Words & Symbols

ENGLISH: 1. as defined in #1 above.

APPLICATION: (see list 280)

This is an editer version of a page from the dictionary MATH SPOKEN HERE!, published in 1995 by MATHEMATICAL CONCEPTS, inc., ISBN: 0-9623593-5-1.

 © 2005, 2022, 2023, Agnes Azzolino www.mathnstuff.com/math/spoken/here/1words/i/i25.htm