AP EAMCET202022 Sep 2020Morning ShiftMathematicsFunctionsActual
The range of the function f(x)=x^2+ 1 x^2+1 is
Options
- A[1, )
- B[2, )
- C[ 3 2 , )
- D(0,1]
Correct answer
A. [1, )
Step-by-step solution
Given function f(x)=x^2+ 1 x^2+1 =y (let) aligned & x^4+x^2+1=y (x^2+1 ) and y>0 & x^4+(1-y) x^2+(1-y)=0 aligned x R , so discriminant 0 array lr & (1-y)^2-4(1-y) 0 & (1-y)(1-y-4) 0 & (1-y)(-3-y) 0 & (y+3)(y-1) 0 y (- ,-3] [1, ) array but y>0 , so y [1, ) Therefore range of f is [1, )