InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Find the rang of`f(x)=(x^2+34 x-71)/(x^2+2x-7)``f(x)=(x^2-x+1)/(x^2+x+1)` |
|
Answer» Correct Answer - `(a) (-infty, 5 )cup [9, infty)` `[1//3,3]` Let `(x^(2) 34 x - 71)/(x^(2) + 2x - 7) = y` or `( 1 - y) + 2(17 - y) x + (7y - 71) = 0` For real value of x `b^(2) - 4ac ge 0` `rArr y^(2) - 14 y + 45 ge 0` `rArr (y - 5) (y - 9) ge 0` `rArr y le 5 or y ge 9` Hence, the range is `(- infty, 5] cup [ 9, infty)` (b) Let `y= (x^(2) - x + 1)/(x^(2)+ x + 1)` `(1 -y )x^(2) - 4 ( 1 - y)^(2) ge 0` Now, if x is real, then `D ge 0` `rArr ( 1 + y)^(2) - 4 (1 - y )^(2) ge 0` or `(1 + y - 2 + 2y) ( 1 + y + 2 - 2y) ge 0` or `(3y - 1) ( 3 - y) ge 0` or ` 3(y - (1)/(2))^(2 )(y - 3) le 0` or `(1)/(3) le y le 3` Hence, the range is `[1//3, 3)].` |
|