Question

Which expression is equivalent to (fg)(5)?

Option 1: f(5)*g(5)
Option 2: f(5)+ g(5)
Option 3: 5f(5)
Option 4: 5g(5)

Answer 1

The correct expression equivalent to (fg)(5) is Option 1: f(5) * g(5).

Step-by-step explanation:

In mathematics, the notation (fg)(x) represents the composition of two functions f and g, denoted as f(g(x)). When evaluating (fg)(5), it means substituting 5 into the composed function. To find this, we first evaluate g(5) and then substitute this result into f(x).

Let's break it down:

1. Evaluate g(5): This involves plugging in 5 as the input for function g. Let's denote this as g<sub>5<sub>: g<sub>5<sub> = g(5).

2. Substitute g<sub>5<sub> into f(x): Now, take the result g<sub>5<sub> and substitute it into f(x). The composed function (fg)(5) is expressed as f(g<sub>5<sub>).

So, the final expression becomes f(5) g(5), making Option 1 the correct choice.

In summary, the composition of functions involves applying one function to the result of another. In this case, evaluating (fg)(5) requires finding g(5) first and then substituting that result into f(x), resulting in f(5) g(5). This aligns with Option 1, providing the correct expression for (fg)(5).