Which is the domain and range of f(x) = -3sqrt (x+2) - 6?

Jul 17, 2018

Domain: $x \ge - 2 \mathmr{and} \left[- 2 , \infty\right)$
Range : $f \left(x\right) \le - 6 \mathmr{and} \left(- \infty , - 6\right]$

Explanation:

$f \left(x\right) = - 3 \sqrt{x + 2} - 6$ . Domain: Possible input value of $x$.

Under root should be >0 ; f(x) is undefined at $x + 2 < 0$

$\therefore x + 2 \ge 0 \mathmr{and} x \ge - 2$ . Therefore domain is

$x \ge - 2 \mathmr{and} \left[- 2 , \infty\right)$ . Range: Possible output of $f \left(x\right)$

for input x ; sqrt(x+2)>=0:. f(x) <= (-3*0) -6 :.

Range : $f \left(x\right) \le - 6 \mathmr{and} \left(- \infty , - 6\right]$

graph{-3 sqrt(x+2) -6 [-40, 40, -20, 20]} [Ans]