The image you've uploaded contains a table related to the composition of two functions, $f(x)$ and $g(x)$, with questions on identifying the inside function and determining the equivalent expressions for function compositions.

Let me break down the content:

Row 1:

• The question asks for the inside function of $f(g(x))$.
• Answer: The inside function is $g(x)$, as it is the function applied first in this composition.

Row 2:

• The question asks for the inside function of $f(x) \circ g(x)$ (composition notation).
• Answer: Again, the inside function is $g(x)$, as it is the function applied first.

Row 3:

• The question asks which expression is equivalent to $f(x) \circ g(x)$ when $f(x) = x + 1$ and $g(x) = 2x$.
• To find the equivalent expression, substitute $g(x) = 2x$ into $f(x)$. So, $f(g(x)) = f(2x) = 2x + 1$.
• Answer: The equivalent expression is $2x + 1$.

Would you like further clarification or have any questions on this? Here's a few related questions to explore:

1. How would you differentiate the composition of functions?
2. What happens when the inside and outside functions are the same?
3. Can you solve for $x$ in a function composition?
4. How do we find the domain of a function composition?
5. How can we apply this concept to real-world problems, such as physics or economics?

Tip: When working with function compositions, always identify which function is inside and which is outside to avoid mistakes in substitution!