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Given that [tex]$f(x)=x+3[tex]$[/tex] and [tex]$[/tex]g(x)=x^2-x[tex]$[/tex], find [tex]$[/tex](f+g)(-6)$[/tex], if it exists.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. [tex]$(f+g)(-6) = \square$[/tex] (Simplify your answer.)
B. The value for [tex]$(f+g)(-6)$[/tex] does not exist.



Answer :

GinnyAnswer
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]

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