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, 1/2) ( b) (-5,-1/5) ( c) (0,1/3 ) (d) [ -1/2 , 0 ) ( e) (-oo - 1/3 ] cup [ 1/4 , oo) `

Explanation

(a) `2 lt x lt 5`
` rArr 1/2 gt 1/xgt1/5`
`rArr 1/(x)in(1/5,1/2)`
(b) `-5 le x lt -1`
`rArr -1/5 ge 1/x gt-1`
`rArr 1/(x)in(-1,-1/5]`
(c) `x gt3 or 3 lt x lt oo`
`x le -2 or - oo lt x le-2`
`rArr 0 gt1/xge-1/2`
`rArr 1/x""in[-1/2,0)`
(e ) `x in [-3 4]or -3 le x le 4`
Now for `1/x `to get defined ,we must have `-3 le x lt 0 ` or `0 lt x le 4`
`rArr -1/3 ge 1/xgt -ooor 1/4 le 1/x""lt oo`
`rArr 1/x""in(-oo,1/3]cup[1/4,oo)`