The problem in the image involves function composition. We are given two functions:

$F(x) = \frac{2x}{x + 3} \quad \text{and} \quad G(x) = x - 1$

We are tasked with finding $(F \circ G)(x)$, which is the composition of $F$ and $G$, i.e., $F(G(x))$.

Step-by-step solution:

1. Substitute $G(x) = x - 1$ into $F(x)$:

$F(G(x)) = F(x - 1)$

2. Use the definition of $F(x) = \frac{2x}{x + 3}$:

Now, substitute $x - 1$ wherever there is $x$ in $F(x)$:

$F(x - 1) = \frac{2(x - 1)}{(x - 1) + 3}$

3. Simplify the expression:

$F(x - 1) = \frac{2(x - 1)}{x - 1 + 3} = \frac{2(x - 1)}{x + 2}$

Expand the numerator:

$F(x - 1) = \frac{2x - 2}{x + 2}$

This is the formula for $(F \circ G)(x)$.

Answer:

The correct formula for $(F \circ G)(x)$ is:

$\boxed{c) \frac{2x - 2}{x + 2}}$

Would you like any additional details or explanations?

Here are 5 related questions you could explore:

1. How do you evaluate the composition of two functions in general?
2. What happens if $G(x) = x + 2$ instead of $x - 1$?
3. Can the composition of functions be reversed, i.e., $(G \circ F)(x)$?
4. How does function composition differ from simple multiplication of functions?
5. Can $F(x)$ or $G(x)$ ever lead to an undefined expression for certain values of $x$?

Tip: When composing functions, always substitute carefully and simplify the resulting expressions step by step!