To determine which expression is equivalent to [tex]\((f g)(5)\)[/tex], we need to consider the operations represented by the notation.
In mathematical function notation, when we see [tex]\((f g)(x)\)[/tex], it usually implies a combined operation involving the functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex] at the same point [tex]\(x\)[/tex]. In this specific case, it is likely asking for the product of the functions evaluated at 5.
Let's evaluate each given option:
1. [tex]\(f(5) \times g(5)\)[/tex]:
- This means we first evaluate [tex]\(f\)[/tex] at 5, then evaluate [tex]\(g\)[/tex] at 5, and finally multiply the two results.
2. [tex]\(f(5) + g(5)\)[/tex]:
- This means we first evaluate [tex]\(f\)[/tex] at 5, then evaluate [tex]\(g\)[/tex] at 5, and finally add the two results.
3. [tex]\(5 f(5)\)[/tex]:
- This means we first evaluate [tex]\(f\)[/tex] at 5 and then multiply the result by 5.
4. [tex]\(5 g(5)\)[/tex]:
- This means we first evaluate [tex]\(g\)[/tex] at 5 and then multiply the result by 5.
Given the notation [tex]\((f g)(5)\)[/tex] and the algebraic properties of function operations, the most appropriate interpretation is that [tex]\((f g)(5)\)[/tex] represents the product of the two function evaluations.
Hence, the correct choice is:
[tex]\[ f(5) \times g(5) \][/tex]
Therefore, the expression equivalent to [tex]\((f g)(5)\)[/tex] is:
[tex]\[ f(5) \times g(5) \][/tex]
