Mathematics

1.2 FUNCTIONS

1. Function is a special relation where every object in a domain has only one image. A function is also known as a mapping.


2. From the types of relation we have learned, only one to one relation and many to one relation are
   function.

Function notation

Small letter: f, g, h or something else…
f : x → 2x
Read as function f map x onto 2x

Example :

Example 1 :

1. Given function f : x →3x − 2 . Find

If the given is object, so we are going to
find the value of image. -1 is the object
because we have to find the value of its
image.

(a) the image of –1

f(x) = 3x – 2
f(-1) = 3(– 1) – 2
        = – 3 – 2
        = – 5

(b) object which has the image 4

If the given is image, so we are going to find
the value of object. 4 is the image because we
have to find the value of its object.

2. Given that f(x) = px + 3 and f(4)= 5. Find the value of p.

From the information given, we know
that 4 is the object and 5 is the image.
The both function is compared because
they are under the same function or in
other way there are having the same
object which is 4. So the value of p can be calculated.

Example 2:

(a) image of 4.
(b) the value of x such that the function g is undefined.

Any number that is divided by zero will result
undefined or infinity. The value of denominator
cannot equal to zero because it would cause
the solution becomes undefined or infinity. To
find the value of x to make the function
undefined, the denominator must be equal to
zero.