**4 Basic Concepts You Need To Learn About Functions**

Basically there are four concepts you need to master in this chapter:

**Relations****Functions****Composite Functions****Inverse Functions**

**Relations**

**Example 1: P is the set of positive even number less than 10.**

** Answer: P = {2,4,6,8}**

It could be explained that the** elements** for the set of { 2,4,6,8 } shared the

**of positive even number which is less than 10.**

*common characteristics*We can say that

relationsexist between set X and Y, when elements of set X was mapped to elements of set Y.

- Set
**X**is the**domain**of the relation, and 1,2,3 is the**object** - Set
**Y**is the**codomain**of the relation, and 1,4,9 is the**image** - The
**range**is the subset of codomain which contains all the images that have been mapped, in this case the range = {1,4,9} - We can also write it as a
**set of ordered pairs**= {(1,1),(2,4),(3,9)} - or represent the relation using a
**graph**as below:

There are **four** types of relations:

**1 to 1 –**1 object being mapped to 1 image

**1 to many**– at least 1 object having*more than 1 image (1 object to many images)*

**many to 1**–*more than 1 object*being mapped to same image (*many objects to 1 image*)**many to many**– at least 1 object having more than 1 image, and more than 1 object being mapped to the same image. (*many objects to many images or vice versa*)

**Functions**

**Example 2 : f (x) –> ****x ^{2 }**

**OR f(x) = x**

^{2 }We can explain the function by using diagram above. A function f take x=3 as input and output as 9. In short, Function f which is x^{2} can be treated as a “**machine**” that converts the input (3) into the output (9).

Only

1 to 1andmany to 1relations are functions

**Composite Functions**

Composite functions could be explained as two functions f and g being combined, and become g[f(x)]. Refer diagram above, it can be visualized as the combination of two “machines”. The first “machine” takes input *x* and outputs *f*(*x*). The second “machine” takes *f*(*x*) and outputs *g*(*f*(*x*)).

In this case,** 3 –> [machine 1] –> 9 –> [machine 2] ****–> 10**

From the diagram, we know that **f (x) –> x ^{2} **and

**g(x) –> x + 1,**so we can find out the composite function of

**gf**as below:

**gf(x) = g[f(x)]**

** = g(x ^{2} )**

**= x**

^{2}+ 1if 3 given as the input (x=3), then

gf(3) = 3** ^{2} **+ 1

=

**10**

**Inverse Functions**

If given a function f(x) = y, then the inverse function is f ^{-1 }(y) = x.

We will discuss some of the questions which are commonly come out in the SPM exam in the topic **SPM Questions for Functions**.

Hey would you like to help me out in mathematics.

If you don’t mind through live chat.

Hi Lucas, you could send me your questions or enquiries to my mailbox: cedriclow(at)perfectmaths.com and we will further discuss your maths problems.