1. State the problem. Problem: Given functions $f : R^+ → R$ defined by $$f(x)=x^2-7$$ and $g : [-3, 2] → R$ defined by $$g(x)=x^2+3$$, compute $(f-g)(-5)$. 2. Formula and rules. The difference of two functions is defined by $$ (f-g)(x)=f(x)-g(x) $$. The domain of $(f-g)$ is the intersection of the domains of $f$ and $g$. For our functions the domain of $(f-g)$ is $R^+ ∩ [-3,2] = (0,2]$. 3. Algebraic simplification and intermediate work. Compute the algebraic difference: $$ (f-g)(x)=(x^2-7)-(x^2+3)=-10 $$. Formally substituting $x=-5$ gives $$ (f-g)(-5)=-10 $$. 4. Domain check and final answer. Since -5 is not in the domain $(0,2]$ the value $(f-g)(-5)$ is undefined even though algebraically the expression simplifies to -10. Therefore the correct choice is (d) undefined.