To determine which expression is equivalent to [tex]\((f \cdot g)(5)\)[/tex], we need to first understand the operation involved.
When we see the notation [tex]\((f \cdot g)(x)\)[/tex], it represents the product of two functions evaluated at [tex]\(x\)[/tex]. Specifically:
[tex]\[
(f \cdot g)(x) = f(x) \cdot g(x)
\][/tex]
For this problem, we are given:
[tex]\[
(f \cdot g)(5)
\][/tex]
Applying the definition of the product of two functions, we evaluate both functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex] at [tex]\(x = 5\)[/tex] and multiply the results:
[tex]\[
(f \cdot g)(5) = f(5) \cdot g(5)
\][/tex]
Therefore, the expression equivalent to [tex]\((f \cdot g)(5)\)[/tex] is:
[tex]\[
f(5) \times g(5)
\][/tex]
Let's verify which of the provided options matches this result:
1. [tex]\(f(5) \times g(5)\)[/tex]
2. [tex]\(f(5) + g(5)\)[/tex]
3. [tex]\(5 f(5)\)[/tex]
4. [tex]\(5 g(5)\)[/tex]
Clearly, the first choice, [tex]\(f(5) \times g(5)\)[/tex], is the correct equivalent expression.
Thus, the correct answer is:
[tex]\[
f(5) \times g(5)
\][/tex]
