To determine which expression is equivalent to [tex]\((f+g)(4)\)[/tex], we need to understand the meaning of [tex]\((f+g)(4)\)[/tex]. This expression represents the value of the function [tex]\( (f+g) \)[/tex] evaluated at [tex]\( x = 4 \)[/tex]. The sum of two functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex] can be written as:
[tex]\[ (f+g)(x) = f(x) + g(x) \][/tex]
So, evaluating this sum at [tex]\( x = 4 \)[/tex] gives us:
[tex]\[ (f+g)(4) = f(4) + g(4) \][/tex]
According to this, we need to add the values of the functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex] when [tex]\( x \)[/tex] is [tex]\( 4 \)[/tex].
Now let's consider each given expression to see if it is equivalent to [tex]\( f(4) + g(4) \)[/tex]:
1. [tex]\( (4) + D(4) \)[/tex]
- There is no function defined as [tex]\( D \)[/tex] in the problem, so this does not match [tex]\( f(4) + g(4) \)[/tex].
2. [tex]\( f(x) + g(4) \)[/tex]
- This expression adds the value of [tex]\( f \)[/tex] at some unspecified [tex]\( x \)[/tex] to the value of [tex]\( g \)[/tex] at [tex]\( 4 \)[/tex]. This is not the same as [tex]\( f(4) + g(4) \)[/tex].
3. [tex]\( \mu(4+g(4)) \)[/tex]
- This expression involves a function [tex]\( \mu \)[/tex], which is not defined, and it doesn't represent the addition of [tex]\( f(4) + g(4) \)[/tex].
4. [tex]\( 4(f(x) + g(x)) \)[/tex]
- This expression simplifies as [tex]\( 4 \)[/tex] times the sum of [tex]\( f \)[/tex] and [tex]\( g \)[/tex] evaluated at some unspecified [tex]\( x \)[/tex]. This is also not equivalent to [tex]\( f(4) + g(4) \)[/tex].
After reviewing each option, we find that none of the given choices directly matches [tex]\( f(4) + g(4) \)[/tex] in the context given.
However, sometimes there might be a formatting issue or interpretation context missing. Please ensure the context and expressions are considered accurately. If we re-evaluate:
The question and attempted solutions might also involve a representation interpretation. Without additional clarifications, consider augmenting the precise evaluation again. Given logical consistency, (none if interpreted directly resolves a pure verification context).
Ultimately, ideally, ensuring representation availability like [tex]\(f(4)+g(4)\)[/tex].
