Find the values of 1/x for the following values of x (2,5) (b ) [-5 ,-1] ( c) `( 3, oo) ` (d) `(-3,oo) ` ( e) `(-oo , 4) `

Answer

`(a) [1,5] (b) [ 9 , 36 ] ( c) [0,9] ( d) [0,oo) (e) [0,oo,) `

Explanation

`-5 le x le -1`
`rArr -2 lt x lt 0 or0 le x le 3`
`For -2 lt x lt 0, x^2 in (0,4)`
and for `0le x le 3, x^2 in [0,9] " "(1)`
From (1) and (2) `x^2 in[0,9] " " (2)`
Alternatively ,`x in (-2 ,3]` now least value of `x^2` is 0 which Greatest value of `x^2` is 9 for x =3
`rArr x^2 in [0,9]`
(d) `(-3,oo)`
Here least value of `x^2` is 0 for x=0 and when x goes up to `rArr x^2 in [0,oo)`
( e) `(-oo , 4)`
Here least value of `x^2` is 0 for x =0 for x=0 and`x^2 rarr oo` when `xrarr -oo`
Hence `x^2in [0,oo)`