How do you find the domain and range of $f(x) = -sqrt(2x + 4) + 3$ ?

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Answer 1 · 2018-07-02T11:37:06

Domain: $x >= -2 or [-2, oo)$
Range: $f(x) <= 3 or [3, -oo)$

$f(x) = -sqrt (2 x+4)+3$

Domain : Possible input of $x$ . Under root is undefined at $<0$ ,

so it must be $>=0 :. 2 x +4 >=0 or 2 x >= -4 or x >= -2$

Domain: $x >= -2 or [-2, oo)$

Range: Possible output value of $f(x) ; sqrt (2 x+4)>=0$ .

Range: $f(x) <= 3 or [3, -oo)$

graph{-(2 x+ 4)^0.5+3 [-10, 10, -5, 5]} [Ans]

How do you find the domain and range of f(x) = -sqrt(2x + 4) + 3f(x) = -sqrt(2x + 4) + 3?