Functions in Mathematics

Functions in MathematicsFunction is described as follows, function is a relationship between range and domain. Thinking about two sets A and B. We form the Cartesian product, we form relations. From all the relationships, we can pick a few which fulfill the rule that each component of the set A is linked to only one element of the set B. When a relation fulfills this rule, it is referred to as a function.

In this chapter, we are going to study how a function is a relation, however a relation might not be a function. Therefore, the function calculator sections assists to differentiate relation and a function. If f is a function from A → B and described as f(a) = b then a = A and b = f(a) = B is unique. A is domain and B is co domain or we can say it as Range of function f. Also, we can state that f from A to B is a relation and each relation from A to B is not a function. 

Note: f is a set of ordered sets, no two of which have the identical first coordinate.

The general notation of a function is actually y = f(x). It is also denotes as f : X ? Y in which, f is the function described between X and Y where, x is in X and y is in Y.

Characteristics of Functions

You can find several characteristics of functions, we will look at them below.

1. Odd and Even functions

A function can be odd or even.

We state a function is odd if they are symmetrical of a point, generally the origin. Such a graph when rotated through 180° about the origin (or the point of symmetry) will give the original graph.

For an odd function, f(-x)= - f(x), for all values of x in the domain.

A function is considered even if it is symmetric about the y-axis. The curve features a line of symmetry about the y-axis and will seem like a reflection of itself along the y-axis.

For an even function, f(-x) = f(x), for all values of x in the domain.  

Examples of odd and even functions:

To learn if a function f(x) is even or odd, we have to find out what occurs when it is turned to f(-x).

If f(-x) is the identical as f(x), i.e. f(-x) = f(x), then it is an even function.

And if f(-x) becomes -f(x), i.e. f(-x) = -f(x), then it is an odd function.

1. f(x) = x4 + x2 + 2

f(-x) = (-x)4 + (-x)2 + 2  =  x4 + x2 + 2

f(-x) is the same as f(x). Hence this is an even function.

A useful tip to remember is that even functions will all have even powers in the function.

2. f(x) = x3 + 3x

f(-x) = (-x)3 + 3 (-x)

= -x3 - 3x

= – (x3 + 3x)

= -f(x)

So f(x) = x3 + 3x is an odd function.

Odd functions will have odd powers in the function.

Types of Functions

You can find some basic types of functions

Surjective Functions:

Surjective function is also known as onto function. Here, every elements in the range is related to a minimum of one element in the domain. If y is element in range then there is a x such that y = f(x).

Injective Functions:

It is also known as one to one function. It fulfills the property that if f(a) = f(b) then, a = b. This is the condition with regard to injective function

Inverse Functions:

If f is a function from A to B then inverse of a function is the function defined from B to A.

It is denoted by f -1. That is, if f:A -> B then f -1 : B -> A. If f(x) = y then x = f-1(y).

Bijective Functions:

If the given function is both injective and surjective or one to one and onto then, it is known as a bijective function.

Latest Articles

Interesting Facts about Platinum

Scientists analyzed samples of the metal following European exploration of the region started. Platinum has been used by ancient people in Central and South America.

Cool Facts about Gold

Not many chemicals can attack gold, so that’s why it maintains it shine even when buried for 1000’s of years. When compared with other metals, gold is much softer. One can beat 1 gram of gold to a 1 square meter sheet and light would shine via that sheet.

Interesting Facts about Wind Energy

One wind turbine can power as much as 500 homes. Wind mills date all the way back to the year 2000 BC where they were utilized in China.

Interesting Facts about Fruit

Fruit is beautiful, tasty and great for all us. Fruit is also interesting. Listed here is a brief collection of interesting facts about fruit.

Facts about the Rock Cycle

Liquid rock which cools quickly after exposure to the Earth’s atmosphere are fine-grained and known as extrusive. Obsidian is an example of this kind of rock.