Question

Arrange the expressions in ascending order of their values when x = -2.
1-x^2/1-2x
x^2-1/1-2x
2x^2+x/2
3x^2+1/2(x-1)

Answer 1

Step-by-step explanation:

Option (1)

$\dfrac{1-x^2}{1-2x}$

Put x = -2, let the value is y such that,

$y=\dfrac{1-(-2)^2}{1-2(-2)}\\\\=\dfrac{1-4}{1+4}\\\\=-0.6$

Option (2)

$\dfrac{x^2-1}{1-2x}$

Put x = -2, let the value is y such that,

$y=\dfrac{(-2)^2-1}{1-2(-2)}\\\\=\dfrac{4-1}{1+4}\\\\=0.6$

Option 3)

$2x^2+\dfrac{x}{2}$

Put x=-2 such that,

$y=2(-2)^2+\dfrac{(-2)}{2}\\\\=7$

Option (4)

$3x^2+\dfrac{1}{2(x-1)}$

Put x =-2 such that,

$y=3(-2)^2+\dfrac{1}{2((-2)-1)}\\\\=11.83$

Ascending values : -0.6,0.6,7,11.83

or

$\dfrac{1-x^2}{1-2x}$   <  $\dfrac{x^2-1}{1-2x}$   <   $2x^2+\dfrac{x}{2}$   <   $3x^2+\dfrac{1}{2(x-1)}$