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

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.

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