AP EAMCET20225 Jul 2022Evening ShiftMathematicsFunctionsActual
The range of the real valued function f ( x )= x^2+x+1 x is
Options
- A(- , 1) (1, )
- B(- ,-1] [1, )
- C(- ,-2] [3, )
- D(- ,-1] [3, )
Correct answer
D. (- ,-1] [3, )
Step-by-step solution
y= x^2+x+1 x aligned & y x=x^2+x+1 & x^2+(1-y) x+1=0 aligned f(x) is real valued function i.e., x R aligned & D 0 & (1-y)^2-4(1)(1) 0 & 1+y^2-2 y-4 0 & y^2-2 y-3 0 & y^2-3 y+y-3 0 & y(y-3)+1(y-3) 0 & (y+1)(y-3) 0 & y (- ,-1] [3, ) & Range of f(x) is (- ,-1] [3, ) aligned