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

1 Answer
Teddy
Jun 24, 2018

Domain: x in(-oo,2]uu[3,oo)x∈(−∞,2]∪[3,∞), Range: yin[0,oo)y∈[0,∞)

Explanation:

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

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