can someone please explain this to me i am confused and don't know what to do

Question

Suppose that the function g is defined , for all real numbers, as follows
g(x)={1/4x-1 if x≤-2
{ -(x-1)^ +3 if -2<x≤2
{ 3 if x>2
g(1)=
g(2)=
g(5)=

Answer 1

I assume a typo, and that
g(x) = -(x-1)^2 + 3 if -2 < x <= 2
just look at the data:

since -2 < 1 <= 2,
g(1) = -(1-1)^2 + 3 = 0+3 = 3

since -2 < 2 <= 2,
g(2) = -(2-1)^2 + 3 = -1+3 = 2

since 5>2,
g(5) = 3

Don't let all the symbols confuse you. Each just tells a part of the story of how g(x) is defined.