To solve for \((f+g)(-6)\), we need to evaluate the functions \(f(x)\) and \(g(x)\) individually at \(x = -6\), then add the results. Here are the detailed steps:
1. Evaluate \(f(x)\) at \(x = -6\):
[tex]\[
f(x) = x + 3
\][/tex]
Substituting \(x = -6\) into \(f(x)\):
[tex]\[
f(-6) = -6 + 3 = -3
\][/tex]
2. Evaluate \(g(x)\) at \(x = -6\):
[tex]\[
g(x) = x^2 - x
\][/tex]
Substituting \(x = -6\) into \(g(x)\):
[tex]\[
g(-6) = (-6)^2 - (-6) = 36 + 6 = 42
\][/tex]
3. Add the results from the evaluations of \(f(-6)\) and \(g(-6)\):
[tex]\[
(f + g)(-6) = f(-6) + g(-6)
\][/tex]
[tex]\[
(f + g)(-6) = -3 + 42 = 39
\][/tex]
Hence, the value for \((f+g)(-6)\) is \(\boxed{39}\). Therefore, the correct choice is:
[tex]\[ \boxed{A. (f+g)(-6)=39} \][/tex]
