Math

Math ?y2 implies that x1 ?x2 . In simpler terms , a function is a set of ed pairs with each element of X paired with a unique element of Y . This is denoted by F : X ?Y with the set X as the domain and the set Y as the range . These sets may not necessarily be numbers

The inverse of a function f (x ) denoted by f-1 (x ) is a function that undoes ' the function by taking the value of f (x ) as the argument x and vice versa . Mathematically , it is written as

p f-1 (x (y , x (x , y ? f (x . It is important to note that in for f-1 (x ) to exist , f (x ) must be a one-to-one (injection ) function that is , no two different elements of the domain will have the same element of the range (if x1 ?x2 then f (x1 ? f (x2 , or if f (x1 f (x2 then x1 x2 ZH

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is true with the cubic function and the exponential function with its inverse logarithmic function

Inverse functions play great importance in the field of mathematics . Not all problems have the same data or information given , hence a need to transform and manipulate the formula to obtain the desired result . This transformation is the inverse of the function

Reference

Mathematics Tutorials and Problems (with Applets . Inverse Functions Retrieved September 3 , 2007 from http /www .analyzemath .com

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Math

h -1 (x x

hf (x x

y

x

Linear function

Cubic function

Cubic function

Cube root function (inverse of cubic function

f-1 (x 3 ?x

f (x x3

Exponential function

g (x ex

function (inverse of exponential function

g-1 (x ln x

l (x x2 , x ? R

Functions without inverses

Quadratic function

Sine function...