we have
![f(x)=\sqrt[]{x+1}-2](https://img.qammunity.org/2023/formulas/mathematics/high-school/ob9a29xl93jv2ei2vny0b1u7n2a4au6prg.png)
In this problem we know that the radicand must be greater than or equal to zero
so
![\begin{gathered} x+1\ge0 \\ x\ge-1 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/7h8sds97we7jlzkj3mse3n2377u6c46j5k.png)
the domain of the function is the interval for x {-1, infinite)
the range is the interval {-2, infinite)
using a graphing tool
see the attached figure
please wait a minute
this is the graph of the function