The problem asks for the composition of two functions $f$ and $g$. The given functions are:

• $f(x) = 2x$
• $g(x) = x + 5$

1. Finding $(f \circ g)(x)$, i.e., $f(g(x))$:

This means we substitute $g(x)$ into $f(x)$.

$f(g(x)) = f(x+5) = 2(x+5) = 2x + 10$

Thus, $(f \circ g)(x) = 2x + 10$.

2. Finding $(g \circ f)(x)$, i.e., $g(f(x))$:

This means we substitute $f(x)$ into $g(x)$.

$g(f(x)) = g(2x) = 2x + 5$

Thus, $(g \circ f)(x) = 2x + 5$.

3. Finding $(f \circ g)(2)$:

Here, we need to calculate $(f \circ g)(x)$ when $x = 2$.

We already know that $(f \circ g)(x) = 2x + 10$.

$(f \circ g)(2) = 2(2) + 10 = 4 + 10 = 14$

Thus, $(f \circ g)(2) = 14$.

Would you like further details or have any questions?
Here are 5 related questions to extend this topic:

1. What is the general formula for the composition of functions?
2. How do we find the inverse of a composed function $f \circ g$?
3. Can we always reverse the order of composition, i.e., $f \circ g = g \circ f$?
4. How do you determine the domain of a composed function?
5. What are some real-world applications of function compositions?

Tip: When working with function compositions, always substitute one function fully into the other to avoid errors in simplification.