# finding the range for the functions

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• December 12th 2009, 05:29 AM
mike--1988
finding 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
• December 12th 2009, 05:42 AM
mathaddict
Quote:

Originally Posted by mike--1988
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

HI

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

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

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

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

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

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

The other one can be solved using this method too .
• December 12th 2009, 06:18 AM
mike--1988
i dont quite understand the method here
• December 12th 2009, 06:27 AM
mathaddict
Quote:

Originally Posted by mike--1988
i dont quite understand the method here

the idea here is to find the range of y which is also the range of the function . When given an equation ,knowing that its roots are real , do you know how to find its discriminant ?
• December 12th 2009, 06:37 AM
mike--1988
ive looked over it again and i understand it now , thank you (Rock)