Question

How do you find the domain and range for `y = sqrt(x^2 -3x +2)`?

Answer 1

Domain: `x <= 1 and x >=2 or x| (-oo,1] uu [2,oo)`
Range: `y >=0 or y| [0,oo)`

Explanation:

`y= sqrt(x^2-3x+2) = sqrt((x-1)(x-2));` Domain: under

root should be `>=0 :. (x-1)(x-2)>=0`

When `1 < x < 2` sign of `y` is `(+)(-) = (-) :. < 0`

Therefore for `1 < x < 2 ; y` is undefined .

Domain: `x <= 1 and x >=2 or x| (-oo,1] uu [2,oo)`

Range: `y >=0 or y| [0,oo)` since square root of positive quantity

is also positive.

graph{(x^2-3x+2)^0.5 [-10, 10, -5, 5]}