To find [tex]\((f+g)(x)\)[/tex] for the given functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex], follow these steps:
1. Identify the functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[
f(x) = 2x + 7
\][/tex]
[tex]\[
g(x) = 7x - 4
\][/tex]
2. Add the functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[
(f+g)(x) = f(x) + g(x)
\][/tex]
3. Substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[
(f+g)(x) = (2x + 7) + (7x - 4)
\][/tex]
4. Combine like terms:
[tex]\[
(f+g)(x) = 2x + 7x + 7 - 4
\][/tex]
5. Simplify the expression:
[tex]\[
(f+g)(x) = (2x + 7x) + (7 - 4)
\][/tex]
[tex]\[
(f+g)(x) = 9x + 3
\][/tex]
So, the simplified form of [tex]\((f+g)(x)\)[/tex] is:
[tex]\[
(f+g)(x) = 9x + 3
\][/tex]
