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:

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

therefore, we have that:

g(-2) = 3

g(-1) = -2

g(3) = -7/2