When faced with the expression (f g) (5), it may seem confusing at first glance. However, by breaking down the process of evaluating this expression and determining equivalent expressions, we can gain a better understanding of how to simplify complex mathematical expressions.

Evaluating the Expression (f g) (5)

To evaluate the expression (f g) (5), we must first understand that (f g) represents the composition of two functions, f and g. This means that we apply the function g to the input, and then apply the function f to the result. In this case, we are given the input 5. So, we start by applying the function g to 5, which gives us g(5). Then, we apply the function f to the result of g(5), which gives us the final output of (f g) (5).

Determining Equivalent Expressions

When trying to determine equivalent expressions for (f g) (5), it can be helpful to break down the expression into its individual components. One equivalent expression could be f(g(5)), which represents the same composition of functions as (f g) (5). Another equivalent expression could be f ∘ g (5), where the symbol ∘ denotes function composition. Additionally, if we are given specific functions f(x) and g(x), we can substitute these functions into the expression to simplify it further.

In conclusion, the expression (f g) (5) may appear daunting at first, but by understanding the concept of function composition and breaking down the expression into its components, we can confidently evaluate and determine equivalent expressions. This process not only helps in simplifying complex mathematical expressions but also enhances our problem-solving skills in mathematics. By practicing and applying these principles, we can tackle more challenging mathematical problems with ease.