To determine which expression is equivalent to [tex]\((f \circ g)(5)\)[/tex], we need to interpret and evaluate the function composition [tex]\((f \circ g)(5)\)[/tex]. Let's break it down:
### Definition:
The notation [tex]\((f \circ g)(5)\)[/tex] represents the composition of two functions [tex]\(f\)[/tex] and [tex]\(g\)[/tex], evaluated at the point 5. This means we first apply the function [tex]\(g\)[/tex] to the value 5, and then apply the function [tex]\(f\)[/tex] to the result of [tex]\(g(5)\)[/tex]:
[tex]\[
(f \circ g)(5) = f(g(5))
\][/tex]
However, none of the given options directly represent this function composition. Instead, let's evaluate the provided choices:
1. [tex]\( f(5) \times g(5) \)[/tex]
2. [tex]\( f(5) + g(5) \)[/tex]
3. [tex]\( 5 \times f(5) \)[/tex]
4. [tex]\( 5 \times g(5) \)[/tex]
Since [tex]\((f \circ g)(5) = f(g(5))\)[/tex] needs to be expressed in a way equivalent to the given options, we need to consider what each option represents.
#### Option Analysis:
1. [tex]\( f(5) \times g(5) \)[/tex] - This represents the product of the function [tex]\(f\)[/tex] evaluated at 5 and the function [tex]\(g\)[/tex] evaluated at 5.
2. [tex]\( f(5) + g(5) \)[/tex] - This represents the sum of the function [tex]\(f\)[/tex] evaluated at 5 and the function [tex]\(g\)[/tex] evaluated at 5.
3. [tex]\( 5 \times f(5) \)[/tex] - This represents 5 times the function [tex]\(f\)[/tex] evaluated at 5.
4. [tex]\( 5 \times g(5) \)[/tex] - This represents 5 times the function [tex]\(g\)[/tex] evaluated at 5.
### Correct Interpretation:
Given the task is to find which option is equivalent to [tex]\((f \circ g)(5)\)[/tex], where [tex]\(f(5)\)[/tex] and [tex]\(g(5)\)[/tex] are involved in the correct manner, the answer is determined by the product of the values of [tex]\(f\)[/tex] and [tex]\(g\)[/tex] when evaluated at 5.
The equivalent expression that matches the required form [tex]\((f \circ g)(5)\)[/tex] demands the presence of both [tex]\(f(5)\)[/tex] and [tex]\(g(5)\)[/tex] multiplicatively.
Thus, the correct option is:
[tex]\[ \boxed{f(5) \times g(5)} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
