Answer:

Step-by-step explanation:
Given the piecewise defined function;
![f(x)=\mleft\{\begin{aligned}-x-1for\rightarrow x<-1_{} \\ -3\text{for} \\ \sqrt[]{x-2}\text{ for}\rightarrow x\ge2\end{aligned}\mright.\rightarrow-1\leq x<2](https://img.qammunity.org/2023/formulas/mathematics/college/iuxp9mqfe4f0cfi2xmyjerr43innp7k453.png)
a) f(-3)
we want to find the value of f(x) at x=-3.
-3 is less than -1, so it falls within the interval x<-1.

b) f(-1)
-1 falls with the second interval

For this interval, f(x) is always equal to -3.

c) f(2)
2 falls within the last interval.
![\begin{gathered} f(x)=\sqrt[]{x-2} \\ f(2)=\sqrt[]{2-2} \\ f(2)=0 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/s3jvkvzre9hs4a9c5eyqbrsqt3eh4k9wjk.png)
d) f(6)
6 falls within the last interval.
![\begin{gathered} f(x)=\sqrt[]{x-2} \\ f(6)=\sqrt[]{6-2} \\ f(6)=\sqrt[]{4} \\ f(6)=2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/tn4j1eftj7ysxpkht5ybqu1brna8mbtz6e.png)