Question

3if xs-2g(x)=< -(x-1) +2 if -2 1Find g(-2),g(-1), and g (3).g(-2) = 1)g(-1) -Х5?9 (3)

Answer 1

Given the information on the picture, we have the following for the values of -2,-1 and 3:

First, if x = -2, notice that we have the following:

`x=-2\Rightarrow-2\ge-2`

then, we have the first case of the function:

`g(-2)=3`

next, if x = -1, notice that -2 < -1 < 1, then, we have the second case:

`\begin{gathered} g(-1)=-(-1-1)^2+2=-(-2)^2+2=-(4)+2=-2 \\ \Rightarrow g(-1)=-2 \end{gathered}`

finally, for x = 3, we have that 3 is greater or equal than 1, then, we apply the third case:

`\begin{gathered} g(3)=-(1)/(2)(3)-2=-(3)/(2)-2=-(7)/(2) \\ \Rightarrow g(3)=-(7)/(2) \end{gathered}`

therefore, we have that:

g(-2) = 3

g(-1) = -2

g(3) = -7/2