im stuck on these last two questions can anyone please help (Worried)

find the range of these functions for XER

1) 1 / (x^2 + 2)

2)1 / (x^2 + 4x +5)

thanks

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- Dec 12th 2009, 05:29 AMmike--1988finding the range for the functions
im stuck on these last two questions can anyone please help (Worried)

find the range of these functions for XER

1) 1 / (x^2 + 2)

2)1 / (x^2 + 4x +5)

thanks - Dec 12th 2009, 05:42 AMmathaddict
HI

(1) Let $\displaystyle y=\frac{1}{x^2+2}$

$\displaystyle yx^2+2y-1=0$

$\displaystyle b^2-4ac\geq 0$ since $\displaystyle x\in R$

$\displaystyle -4y(2y-1)\geq 0$

$\displaystyle 4y(2y-1)\leq 0$

so $\displaystyle y\in [0,\frac{1}{2}]$

The other one can be solved using this method too . - Dec 12th 2009, 06:18 AMmike--1988
i dont quite understand the method here

- Dec 12th 2009, 06:27 AMmathaddict
- Dec 12th 2009, 06:37 AMmike--1988
ive looked over it again and i understand it now , thank you (Rock)