Answer:
D. [tex]f(-2)=3[/tex]
Step by step explanation:
We have been given a piece wise function:
[tex]f{x}=\left\{\begin{matrix}-x^{2}; &x< -2 \\3;&-2\leq x< 0\\x+2; & x\geq 0\end{matrix}\right[/tex]
We are asked to find value of f(-2).
In our piece function when we will input values of x less than -2([tex]x<-2[/tex]) , it will give us output as [tex]-x^{2}[/tex]
For values greater than or equal to 0 our function will give output as x+2.
We can see from our piece wise function that when x is greater than or equal to -2 and less than 0 our function gives a constant output, that is 3.
Therefore, [tex]f(-2)=3[/tex] and option D is the correct choice.
