InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
The range of the function `f(x)=(x^2+x+2)/(x^2+x+1),x in R ,`isA. `(1,infty)`B. `(1,11//7)`C. `(1,7//3]`D. `(1,7//5)` |
|
Answer» Correct Answer - C Let `y=f(x)=(x^(2)+x+2)/(x^(2)+x+1), x in R` `therefore y=(x^(2)+x+2)/(x^(2)+x+1)` `y=1+(1)/(x^(2)+x+1) " "[i.e. y gt 1]` ...(i) ` rArr yx^(2)+yx+y=x^(2)+x+2` ` rArr x^(2) (y-1) + x(y-1)+(y-2)=0, AA x in R` Since, x is real, `D ge 0` `rArr (y-1)^(2)-4(y-1)(y-2) ge 0` ` rArr (y-1) {(y-1) -4(y-2)} ge 0` `rArr (y-1)(-3y+7) ge 0` `rArr 1 le y le (7)/(3) " ...(ii)" ` From Eqs. (i) and (ii), Range ` in (1,(7)/(3)]` |
|