Question

Find the domain and range of a real function f(x) =1/(1-x^2)

Answer 1

@satellite73 @Rdx

Answer 2

domain x gtreater than equal to 0

Answer 3

till infinity

Answer 4

wat ......confused!!

Answer 5

sorry greater than 1

Answer 6

domain s x!=+/-1

Answer 7

arrey domain is set of numbers that u can put in ur equation so if x=1 u get answer as 1/0 which is unceptable so u can put any number in x except the number which gives u 1

Answer 8

not only 1 -1 aslo!!

Answer 9

so Domain= R-{-1 , 1}

Answer 10

yup

Answer 11

so wat is the range

Answer 12

so wat x2 represents a parabola and 1-x2 tooo

Answer 13

so wat will be range

Answer 14

Do you know what domain and range mean, as vocabulary words?

Answer 15

yup

Answer 16

In your own words, what do they mean?

Answer 17

domain means wat we give and range wat we get

Answer 18

And what is NOT allowed in the domain?

Answer 19

sqrt of negative , denominator 0

Answer 20

Yes. Also natural log of a number less than or equal to zero.

Answer 21

so wat is the range here

Answer 22

range is-infinity to infinity except 0

Answer 23

So looking at \[\huge f(x) =\frac{1}{(1-x^2)}\]

1) Are there any natural logs?
2) Are there any square roots?
3) Are there any expressions in the denominator that could go to zero?

Answer 24

is it R-{0}

Answer 25

is that the range

Answer 26

here expressions in the denominator that could go to zero?

Answer 27

see trying plotting 1-x2 nd u l get an idea

Answer 28

i think i have written the same thing

Answer 29

Oh sorry you've already got the Domain.

Answer 30

@mathteacher1729 help me pls

Answer 31

The range is all output from the function's allowable input.

There are a few ways to find range, one of the easiest is to plot it and see what the graph does.

Answer 32

@Rdx but in my book the asnwer shows as (-infinity , 0) U {1 , infinity)

Answer 33

is both are same R-{0} and (-infinity , 0) U {1 , infinity)

Answer 34

yes i m a lazy butt ur book is correct

Answer 35

both are correct

Answer 36

no i m not

Answer 37

i have included infinity thats not correct

Answer 38

not that i am asking abt is both are same R-{0} and (-infinity , 0) U {1 , infinity)

Answer 39

still or precision sake

Answer 40

do i need to explain range?

Answer 41

No i knw it ......i want to knw is both are same R-{0} and (-infinity , 0) U {1 , infinity)????

Answer 42

The range \[y \in (\infty, 0) \cup [1,\infty)\]

This should be clear from the graph. (attached).

Do you know how to use geogebra to create graphs like this?

Answer 43

The function f(x) = 1 when we let x = 0. The function f(x) approaches 0 , but never reaches zero (Asymptote at zero) as we let x go to + or - infinity.

Answer 44

is there any way to find range without graph

Answer 45

@mathteacher1729 we have to do that with proplr algeric steps, in exam with complex function we cant draw graph

Answer 46

yes 1 sec posting

Answer 47

@Rdx that is true, but that doesn't mean you shouldn't learn to visualize as well. It is a powerful tool that can come in handy on an exam even if you don't have a calculator.

Answer 48

is there any way to find range without graph

Answer 49

@mathteacher1729 indians dont get calculator in exam not even b.tech exam :P