We have that the values of the function g(x) at g(-3), g(-2), and g(-1) is give n as follows
[tex]g(-3)=0.25\\\\g(-2)=-2 \\\\g(-2)=-3[/tex]
Through the calculations below
From the question we are told that:
[tex]g(x)=-\frac{1}{4}x+1[/tex] if [tex]x<-2[/tex]
[tex]g(x)=(x+1)^2-3[/tex] if [tex]-2 \leq x<2[/tex]
Generally we access the variables of g and therefore use the appropriate equation to access g(x) for every given point
For [tex]g(-3)[/tex]
This lies with " if x<-2 "
Therefore
[tex]g(x)=-\frac{1}{4}x+1 \\\\g(-3)=-\frac{1}{4}(3)+1 \\\\g(-3)=0.25[/tex]
For [tex]g(-2)[/tex]
This lies with " if[tex]-2 \leq x<2[/tex] "
Therefore
[tex]g(x)=(x+1)^2-3 \\\\g(x)=((-2)+1)^2-3 \\\\g(-2)=-2[/tex]
For [tex]g(-1)[/tex]
This lies with " if[tex]-2 \leq x<2[/tex] "
Therefore
[tex]g(x)=((-1)+1)^2-3 \\\\g(-1)=-3[/tex]
In conclusion
The value of the function g(x) at g(-3), g(-2), and g(-1) is give as follows
[tex]g(-3)=0.25\\\\g(-2)=-2 \\\\g(-2)=-3[/tex]
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