Option B: 5 is the value of f(3)
Explanation:
The equation of the piecewise function is given by
[tex]f(x)=\left\{\begin{aligned}-x^{2}, & x<-2 \\3, &-2 \leq x<0 \\x+2, & x \geq 0\end{aligned}\right.[/tex]
We need to find the value of [tex]f(3)[/tex]
The value of the function f can be determined when [tex]x=3[/tex] by identifying in which interval does the value of [tex]x=3[/tex] lie in the piecewise function.
Thus, [tex]x=3[/tex] lies in the interval [tex]x\geq 0[/tex] , the function f is given by
[tex]f(x)=x+2[/tex]
Substituting [tex]x=3[/tex] in the function [tex]f(x)=x+2[/tex], we get,
[tex]f(3)=3+2[/tex]
[tex]f(3)=5[/tex]
Thus, the value of [tex]f(3)[/tex] is 5.
Therefore, Option B is the correct answer.
