To determine which expression is equivalent to [tex]\((f g)(5)\)[/tex], we need to understand what that notation represents.
Let's break it down:
1. Understanding [tex]\((f g)(x)\)[/tex]:
- Typically, [tex]\( (f g)(x) \)[/tex] in the context of function composition means [tex]\( f(g(x)) \)[/tex]. However, in this question, we are interpreting [tex]\( (f g)(x) \)[/tex] as the multiplication of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex].
- Therefore, [tex]\( (f g)(5) \)[/tex] would mean [tex]\( f(5) \times g(5) \)[/tex].
2. Analyzing the given options:
- [tex]\( 5 g(5) \)[/tex]: This means multiplying 5 by the value of function [tex]\( g \)[/tex] at 5. This is not the same as what we need.
- [tex]\( f(5) \times g(5) \)[/tex]: This is exactly the expression we are looking for, as it represents the product of the value of [tex]\( f \)[/tex] at 5 and the value of [tex]\( g \)[/tex] at 5.
- [tex]\( 5 f(5) \)[/tex]: This means multiplying 5 by the value of function [tex]\( f \)[/tex] at 5. This is not the same as what we need.
- [tex]\( f(5) + g(5) \)[/tex]: This means adding the value of function [tex]\( f \)[/tex] at 5 to the value of function [tex]\( g \)[/tex] at 5. This is not the same as what we need.
3. Conclusion:
- The expression that is equivalent to [tex]\((f g)(5)\)[/tex] is [tex]\( f(5) \times g(5) \)[/tex].
Therefore, the correct choice is:
[tex]\[ \boxed{f(5) \times g(5)} \][/tex]
