Find the domain and range of the function.
-$f ( x ) = \frac { 2 } { 2 + \sqrt { x } }$
A) D: $[ 0 , \infty )$, R: $( 0,1 ]$
B) D: $( - \infty , 0 ] , R : ( - \infty , 0 ]$
C) D: $[ 0 , \infty )$, R: $( - \infty , \infty )$
D) D: $( - \infty , \infty ) , R : ( 0,1 ]$

Question

Quizplus · Accepted Answer

- To find the domain of the function, we need to look at the denominator. The square root of a negative number is not defined in the real numbers, so x cannot be negative. Therefore, the domain is all non-negative real numbers: $[ 0 , \infty )$.
- To find the range of the function, we need to analyze the behavior of the function as x changes. As x increases without bound, the function approaches 1, since the denominator grows at the same rate as the numerator. On the other hand, as x approaches 0 from the right, the function approaches 0, since the denominator becomes much larger than the numerator. Therefore, the range of the function is all real numbers greater than 0 and less than or equal to 1: $(0,1]$.

Find the Domain and Range of the Function f(x)=22+xf ( x ) = \frac { 2 } { 2 + \sqrt { x } }f(x)=2+x​2​

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