Find the domain and range of the function.
-$$f ( x ) = - 2 + \sqrt { x }$$
A) D: $( - \infty , 0 ]$, R: $( - \infty , - 2 ]$
B) D: $[ 0 , \infty ) , R : [ - 2 , \infty )$
C) D: $( - \infty , \infty )$, R: $[ - 2 , \infty )$
D) D: $[ 0 , \infty )$, R: $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The domain must satisfy two conditions: 
1) The expression under the square root must be nonnegative 
2) The value inside the square root cannot be negative

Solve the inequality $x\geq 0$ to find the domain.

$$x\geq 0$$
$$x^{\frac{1}{2}}\geq 0$$

Therefore, the domain is $[0,\infty)$.

Since $\sqrt{x}$ outputs a nonnegative value, the minimum value of $f(x)$ is $-2$ which occurs at $x=0$.

Therefore, the range of the function is $[-2, \infty)$.

The only answer choice that includes the correct domain and range is B.

Find the Domain and Range of the Function f(x)=−2+xf ( x ) = - 2 + \sqrt { x }f(x)=−2+x​

Find the Domain and Range of the Function $f ( x ) = - 2 + \sqrt { x }$