Answered

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Which expression is equivalent to [tex]\((f \cdot g)(5)\)[/tex]?

A. [tex]\( f(5) \times g(5) \)[/tex]

B. [tex]\( f(5) + g(5) \)[/tex]

C. [tex]\( 5 f(5) \)[/tex]

D. [tex]\( 5 g(5) \)[/tex]

Sagot :

GinnyAnsweridn
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]
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