Question

F(x)=\sqrt(x^(2)-5x+6), find the domain and range ?

Answer 1

Domain: `x in(-oo,2]uu[3,oo)`, Range: `yin[0,oo)`

Explanation:

To find the domain, we will factor the quadratic expression in the square root to get `F(x)=sqrt((x-2)(x-3))`.

Assuming `F:RR->RR`, we know that `(x-2)(x-3)>=0`. Consider `x<2`: we have `("negative")("negative")="positive">=0`.
Consider `2< x <3`: we have `("positive")("negative")="negative"<0`.
Consider `x>3`: we have `("positive")("positive")="positive">=0`.
Therefore, the domain of `F` is `x in (-oo, 2]uu[3,oo)`.

For the range of `F`, we know that the square root function returns non-negative numbers so we know that the range of `F` is `yin[0,oo)`.