To find [tex]\((f+g)(a)\)[/tex], we need to add the functions [tex]\(f(a)\)[/tex] and [tex]\(g(a)\)[/tex] together. Let's proceed with the following steps:
1. Write down the given functions:
- [tex]\(f(a) = -2a + 3\)[/tex]
- [tex]\(g(a) = a - 5\)[/tex]
2. Determine the sum of [tex]\(f(a)\)[/tex] and [tex]\(g(a)\)[/tex]:
- [tex]\((f+g)(a) = f(a) + g(a)\)[/tex]
3. Substitute the expressions for [tex]\(f(a)\)[/tex] and [tex]\(g(a)\)[/tex]:
- [tex]\((f+g)(a) = (-2a + 3) + (a - 5)\)[/tex]
4. Combine like terms:
- Combine the coefficients of [tex]\(a\)[/tex]: [tex]\(-2a + a = -a\)[/tex]
- Combine the constant terms: [tex]\(3 - 5 = -2\)[/tex]
5. Write the resulting expression:
- [tex]\((f+g)(a) = -a - 2\)[/tex]
So, the final expression for [tex]\((f+g)(a)\)[/tex] is:
[tex]\[
(f+g)(a) = -a - 2
\][/tex]
