Given:
The piecewise function is:
[tex]f(x)=\begin{cases}x+5&x<-2\\x^2+2x+3&x\geq -2\end{cases}[/tex]
To find:
The values of [tex]f(-4),f(-2),f(0),f(3)[/tex].
Solution:
For [tex]x<-2[/tex], the function is
[tex]f(x)=x+5[/tex]
For [tex]x\geq -2[/tex], the function is
[tex]f(x)=x^2+2x+3[/tex]
a) The value of [tex]f(-4)[/tex] is:
[tex]f(-4)=-4+5[/tex]
[tex]f(-4)=1[/tex]
b) The value of [tex]f(-2)[/tex] is:
[tex]f(-2)=(-2)^2+2(-2)+3[/tex]
[tex]f(-2)=4-4+3[/tex]
[tex]f(-2)=3[/tex]
c) The value of [tex]f(0)[/tex] is:
[tex]f(0)=(0)^2+2(0)+3[/tex]
[tex]f(0)=0-0+3[/tex]
[tex]f(0)=3[/tex]
d) The value of [tex]f(3)[/tex] is:
[tex]f(3)=(3)^2+2(3)+3[/tex]
[tex]f(3)=9+6+3[/tex]
[tex]f(3)=18[/tex]
Therefore, the required values are [tex]f(-4)=1,f(-2)=3,f(0)=3,f(3)=18[/tex].
