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]



Answer :

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]