range of function

[red and white kop!]

use any method to find the range of the function f, where
1. f(x) = 1/(x-2)(x-6)
2. f(x) = x/(1-x)^2

i really dont know where to start here. i could graph these functions, but i just don't manage to break them down to recognisable patterns. otherwise i thought i could find the domain of the inverse and then use that as the range, but that doesnt work does it? anyway i would be needing some help... :?

 

[BigGlenntheHeavy]

f(x) = 1/[(x-2)(x-6)]

Domain = (-?,2)µ(2,6)µ(6,?), Range = (-?,-1/4]µ(0,?)

f(x) = x/(1-x)^2

Domain = (-?,1)µ(1,?), Range = [-.25,?)

 

[red and white kop!]

can you please show me what method you used to figure this out?

 

[BigGlenntheHeavy]

For the ranges of the respective functions, take their derivatives to find their maxes and mins.

For f(x) = 1/((x-2)(x-6)), see graph below. Other than the gap its range would be (-?,?), as it is, its actual range is (-?,-.25]µ(0,?)

[attachment=0:314isckb]xxx.jpg[/attachment:314isckb]