Question

find domain and range , f(x) = x^2 + 2 , x element of R.

Answer 1

so.....Domain is given in the question....Can u guess

Answer 2

infinity ?

Answer 3

nop... Domain =R

Answer 4

teach me please !

Answer 5

how ?

Answer 6

x element of R. it is given

Answer 7

i knw this is little difficult topic... in chapter 2

Answer 8

@ashna domain is to find x such that for all values of x the function is defined..

Answer 9

yeah ..

Answer 10

Here can you tell the value of x such that the function is not defined??

Answer 11

becoz there is no rational function or sqrt function

Answer 12

more over it is given in the question itself

Answer 13

no i dont understand @waterineyes .. i know explaining well .. but i dont understand .

Answer 14

For every value of x you will get f(x)..

Right @ashna ??

Or you can tell the value of x such that you will get f(x) undefined ??

Answer 15

no !

Answer 16

You have to choose values of x from Real numbers..

For every real number you will get f(x) or not ??

Answer 17

yes we'll get f(x)

Answer 18

So can you tell me what will be the domain ??

Answer 19

all real no's !

Answer 20

Correct..

Answer 21

yea .. understood :)

Answer 22

what about range ?

Answer 23

We represent like this:

\[Domain : \mathbb{R}\]

Answer 24

okay !

Answer 25

For range you will do like:

Let f(x) = y..

Answer 26

can we also write domain as -infinity and +infinity ?

Answer 27

okay !

Answer 28

So:

\[y = x^2 + 2\]

So here can you find x in terms of y ??

Answer 29

Yes you can write that..

Answer 30

there is another way

Answer 31

just plug values for x and see wat u get

Answer 32

yea .. 1^2 + 2 = 3
2^2 + 2 = 6

Answer 33

For range we have to put for y not for x..

Answer 34

nop @waterineyes

Answer 35

Not this way @ashna

Answer 36

x^2 + 2

Answer 37

then ?

Answer 38

wat is the min value of this eq

Answer 39

I said to find y.

Subtract 2 both the sides..

Answer 40

- infinity

Answer 41

u follow @waterineyes

Answer 42

If you think you can explain her then go for it @Yahoo!

Answer 43

why subtract two ?

Answer 44

if u r not getting that i will tell another easy...way we can just figure out this by seeing

Answer 45

You have to find x there..

Answer 46

nop @waterineyes u go on!

Answer 47

sumone decide !

Answer 48

lol. follow waterineyes

Answer 49

See the equation is:

\[y = x^2 + 2\]

Here you have to find x..

How can you find x here??

Answer 50

Don't find the values of x just find x in terms of y..

Answer 51

by substituting any real no in x ?

Answer 52

nuuuuu

Answer 53

No no..

Just in terms of y..

Answer 54

Subtract 2 both the sides..

Answer 55

\[x = \sqrt{y-2}\]

Answer 56

^ trigger happy, mate?

Answer 57

\[y = x^2 + 2\]
Subtract 2:
\[y - 2 = x^2\]

Take square root:

\[x = \sqrt{y-2}\]

Answer 58

okay .. understood and thanks all !

Answer 59

so range is (2, infinity ) ?

Answer 60

yes

Answer 61

Now one thing you must remember that the value inside the square root bracket must not be negative:

So:

\[y - 2 \ge 0\]

yes..

Well Done..

Answer 62

but [2 , infinity

Answer 63

dont forgot which bracket to use

Answer 64

okay :)

Answer 65

[2 , infinity)

Answer 66

Note the brackets @ashna

\[Range : [2, \infty)\]

Answer 67

yeah okay :)

Answer 68

Because this will include 2 also..

Answer 69

okay !

Answer 70

how about the set notation?

Answer 71

Meaning ??

Answer 72

the set-builder notation

Answer 73

Do you know about that???

Answer 74

we used to write this in roster form @panlac01

Answer 75

easy to mention in roster than in set builder

Answer 76

\[\{x: - \infty < x < \infty\}\]
Like this ??

Answer 77

yes, something like that

\[\left\{ x|x \epsilon \mathbb{N} , x<10\right\}\]

Answer 78

in that case it is >=2

Answer 79

or I just need to sleep...