Answer :

To find the value of [tex]\( f(7) + g(5) \)[/tex], we first need to understand the given functions:

1. Function [tex]\( f(x) \)[/tex] is defined as [tex]\( f(x) = 3x - 4 \)[/tex].

Let's calculate [tex]\( f(7) \)[/tex]:
- Substitute [tex]\( x = 7 \)[/tex] into the function.
- [tex]\( f(7) = 3 \times 7 - 4 \)[/tex].
- [tex]\( f(7) = 21 - 4 \)[/tex].
- So, [tex]\( f(7) = 17 \)[/tex].

2. Function [tex]\( g(x) \)[/tex] is defined as [tex]\( g(x) = x^2 + 2 \)[/tex].

Now, let's calculate [tex]\( g(5) \)[/tex]:
- Substitute [tex]\( x = 5 \)[/tex] into the function.
- [tex]\( g(5) = 5^2 + 2 \)[/tex].
- [tex]\( g(5) = 25 + 2 \)[/tex].
- So, [tex]\( g(5) = 27 \)[/tex].

Finally, add the two results to find [tex]\( f(7) + g(5) \)[/tex]:
- [tex]\( f(7) + g(5) = 17 + 27 \)[/tex].
- [tex]\( f(7) + g(5) = 44 \)[/tex].

Thus, the value of [tex]\( f(7) + g(5) \)[/tex] is [tex]\(\boxed{44}\)[/tex].

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