Question

Can u answers the rounded questions

Answer 1

Answer 1:

`(x^(2) -x+1)/(x^(2) +x+1)`

Here given that, x is real that is the domain

Range of the given expression is :

`(1)/(3) \leq y\leq 3`

Write it interval form.

`[(1)/(3),3]` Option (2)

Answer 3:

`(11x^(2) +12x+6)/(x^(2) +4x+2)`

Here domain is all real x.

Range is :

{y ∈ R : y ≤ -5 or y ≥ 3}

In interval form:

(-∞, -5] ∪ [3, ∞)

So, y can't lies between -5 to 3 Option (2)

Answer 5 :

`(x^(2) -3x+4)/(x^(2) +3x+4)`

Here domain is :

x is real

And range is :

{y ∈ R :
`(-1)/(7)` ≤ y ≤ 7}

We see that maximum y value is 7.

So, maximum value is 7. Option (4)

Answer 6:

`\sqrt{9x^(2)+6x+1 } < (2 -x)`

Solve for x .

Square both the side

9x² + 6x + 1 = 4 + x² - 4x

8x² + 10x - 3 < 0

(2x + 3)(4x - 1) < 0

2x + 3 = 0 & 4x - 1 = 0

x =
`(-3)/(2)` & x =
`(1)/(4)`

So,

`(-3)/(2) < x < (1)/(4)`

x ∈
`(-(3)/(2) , (1)/(4) )` Option (1)