# finding the range for the functions

• Dec 12th 2009, 06:29 AM
mike--1988
finding the range for the functions

find the range of these functions for XER

1) 1 / (x^2 + 2)

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

thanks
• Dec 12th 2009, 06:42 AM
Quote:

Originally Posted by mike--1988

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 .
• Dec 12th 2009, 07:18 AM
mike--1988
i dont quite understand the method here
• Dec 12th 2009, 07:27 AM