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

Jul 2, 2018

Domain: $x \ge - 2 \mathmr{and} \left[- 2 , \infty\right)$
Range: $f \left(x\right) \le 3 \mathmr{and} \left[3 , - \infty\right)$

#### Explanation:

$f \left(x\right) = - \sqrt{2 x + 4} + 3$

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

so it must be $\ge 0 \therefore 2 x + 4 \ge 0 \mathmr{and} 2 x \ge - 4 \mathmr{and} x \ge - 2$

Domain: $x \ge - 2 \mathmr{and} \left[- 2 , \infty\right)$

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

Range: $f \left(x\right) \le 3 \mathmr{and} \left[3 , - \infty\right)$

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