Answer:
a) g(-2) = 0
b) g(-1) =1
c) g(4) = 2
Step-by-step explanation:
Given data
[tex]g(x) = \frac{-1}{4x+1} if x < -2[/tex]
[tex]g(x) = - (x+1)^{2} +1 if -2\leq x\leq 2[/tex]
[tex]g(x) = 2 if x >2[/tex]
Step( i ):-
[tex]g(x) = - (x+1)^{2} +1 if -2\leq x\leq 2[/tex]
put x = -2
[tex]g(-2) = -(-2+1)^{2} +1 = -(-1)^{2}+1 = -1+1 =0[/tex]
g(-2) = 0
Step(ii):-
[tex]g(x) = - (x+1)^{2} +1 if -2\leq x\leq 2[/tex]
Put x = -1
[tex]g(-1) = -(-1+1)^{2} +1 = -(0)^{2}+1 = -0+1 =1[/tex]
g(-1) =1
Step(iii):-
[tex]g(x) = 2 if x >2[/tex]
g(4) = 2
