Question

f(x) = sqrt( 1- X^2 ) . f: R -> R

find domain of f?

Answer 1

sqrt( 1- X^2 ) <---- this term for values of X must be a real number.

Answer 2

1 - \[x^{2}\] must be \[\ge\] 0

Answer 3

yes.

Answer 4

omg.

Answer 5

experiment plz solve

Answer 6

\[1 - x^{2}\] >= 0 find all values for x

Answer 7

Oops sorry , i thought x^2 - 1,

Answer 8

try again San..... :)

Answer 9

yeah ... i didn't see that equation properly.

1 - x^2 >=0
1 >= x^2

so x^2 must always be less or equal to one.

it can have that value in betwen -1 and 1, so this is your domain.

it must be x<= 1
{x:x<=1 or x >= -1}
or [-1, 1]

Answer 10

ohh.. i got your answer..

Answer 11

but one thing more...

Answer 12

x^2 <= 1 what if we sqrt both side ?

Answer 13

??

Answer 14

x^2 <= 1 what if we sqrt both side ?

Answer 15

you will get x<= -1
and x <= +1

but -3 will not work on our condition, will it??

Answer 16

the best way to do this would be
x^2 <= 1

or, |x^2| <= 1
or, -1 <= |x^2| <= 1
or, -1 <= x <= 1

Answer 17

but experiment... we know that if we sqrt x^2 we get | x | m i right ?

Answer 18

if we take modulus both sides, doesn't it effect the inequality?

Answer 19

I don't think so.
that would imply
|x| <= 1 and |x| <= -1

Answer 20

in this case yes, it will not affect. because |x^2| and x^2 will always be positive no matter what the value of x is.

Answer 21

unless it's non real.

Answer 22

ohhhh.. i got u :)

Answer 23

thanks :) alot i will be back with new problem :) :) thanks brooooooooooooooooooooooooooooooooooooooo

Answer 24

sure ... you are welcome.