Find-the-domain-of-the-function-and-sketch-the-graph-f-x-2x-1-if-x-lt-0-x-2-if-0-x-2-1-if-x-2-

Question Number 49983 by Tawa1 last updated on 12/Dec/18

Find the domain of the function and sketch the graph

f (x) = {\begin{cases} 2 x - 1, if x < 0 \\ x^{2}, if 0 ⩽ x ⩽ 2 \\ 1, if x ⩽ 2 \end{cases}

Answered by kaivan.ahmadi last updated on 15/Dec/18

this is not a function since f (0.5) = 0.25 for f (x) = x^{2}

and f (0.5) = 1 for f (x) = 1 .

in genral the domain of each criterion must have no intersection

otherwise f is not function

(0 ⩽ x ⩽ 2) \cap (x ⩽ 2) = [0, 2] \neq \emptyset