Question

find the range of function f X equal to X square + X - 1 / X square + 2 X + 3​

Answer 1

Answer:

Correct option is

A

[

3

1

,3]

Let y=

x

2

+x+1

x

2

−x+1

⇒yx

2

+yx+y=x

2

−x+1

⇒(x−1)x

2

+(y+1)x+(y−1)=0

If x∈R, then

Discriminant ≥0

⇒(y+1)

2

−4(y−1)

2

≥0

⇒−3y

2

+10y−3≥0

⇒3y

2

−10y+3≤0

⇒(3y−1)(y−3)≤0

⇒

3

1

≤y≤3

∴ Range =[

3

1

,3]