# Thread: finding the range for the functions

1. ## finding the range for the functions

im stuck on these last two questions can anyone please help

find the range of these functions for XER

1) 1 / (x^2 + 2)

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

thanks

2. Originally Posted by mike--1988
im stuck on these last two questions can anyone please help

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 .

3. i dont quite understand the method here

4. 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 ?

5. ive looked over it again and i understand it now , thank you