Finding the Range for Square Root and Rational Functions | Homework Help

[jwxie]

Homework Statement

find range for f(x) = sqrt of x-1

f(x) 1/x^2-1

Homework Equations

no...

The Attempt at a Solution

well, i know this is dumb to ask, but i am very very curious...

let say the first one, sqrt of x-1
if we want to find the range, obviously, you can tell just by looking at the function, since it is sqrt, it has to be y>0

second function, f(x)= 1/x^2-1
so i tried to use use the x-y method, you replace x with y, and y with x

so it becomes x = 1/y^2-1
now it is my range, but if i want to know the notation interval, like ( infinite, 0), then how do i solve for the range and get some actual indications for the range.

 

[Dick]

Your first and best bet is to draw a graph of each function. Try doing that. Find critical points, the whole bit. And when you post, try and make the nature of the function clear. 1/x^2-1 could mean either (1/x^2)-1 or 1/(x^2-1). I think you mean the latter. And I think your range for the first one should be y>=0 (i.e. include y=0).