1. The problem asks to find the values of $x$ for which $g(x) = 2$ and $g(x) = -3$ given the function $g(x)$ is linear and passes through points $(-1, -1)$ and $(2, 2)$. 2. First, find the equation of the line $g(x)$. The slope $m$ is given by: $$m = \frac{2 - (-1)}{2 - (-1)} = \frac{3}{3} = 1$$ 3. Using point-slope form with point $(-1, -1)$: $$y - (-1) = 1(x - (-1))$$ $$y + 1 = x + 1$$ $$y = x$$ So, the function is $g(x) = x$. 4. For part (a), solve $g(x) = 2$: $$x = 2$$ 5. For part (b), solve $g(x) = -3$: $$x = -3$$ 6. Note that $x = -3$ is outside the given graph range but mathematically valid. Final answers: (a) $x = 2$ (b) $x = -3$