To determine which expression is equivalent to [tex]\((f g)(5)\)[/tex], you need to understand the notation. In this context, [tex]\((f g)(5)\)[/tex] implies the multiplication of [tex]\(f(5)\)[/tex] and [tex]\(g(5)\)[/tex]. Here is the step-by-step reasoning:
1. Identify the Meaning of [tex]\((f g)(5)\)[/tex]:
- The notation [tex]\((f g)(x)\)[/tex] means the product of [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].
2. Substitute [tex]\(x\)[/tex] with 5:
- When [tex]\(x\)[/tex] is substituted by 5, it becomes [tex]\((f g)(5)\)[/tex].
3. Express in Terms of Known Functions:
- This can be written as [tex]\(f(5) \times g(5)\)[/tex].
So, among the given options:
- [tex]\(f(5) \times g(5)\)[/tex] is the correct and equivalent expression for [tex]\((f g)(5)\)[/tex].
Thus, the correct answer is:
[tex]\[ f(5) \times g(5) \][/tex]
