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We are asked to find \( (f \circ g)(x) \), which is the composition of the functions \( f(x) = 5x + 5 \) and \( g(x) = 2x^2 + 7x + 13 \).

To compute \( (f \circ g)(x) \), we need to substitute \( g(x) \) into \( f(x) \). In other words, we replace every \( x \) in \( f(x) \) with \( g(x) \):

\[
(f \circ g)(x) = f(g(x)) = 5(g(x)) + 5
\]

Since \( g(x) = 2x^2 + 7x + 13 \), substitute that into \( f(x) \):

\[
f(g(x)) = 5(2x^2 + 7x + 13) + 5
\]

Now, distribute the 5:

\[
f(g(x)) = 5 \cdot 2x^2 + 5 \cdot 7x + 5 \cdot 13 + 5
\]

This simplifies to:

\[
f(g(x)) = 10x^2 + 35x + 65 + 5
\]

Combining the constant terms:

\[
f(g(x)) = 10x^2 + 35x + 70
\]

Thus, the composition \( (f \circ g)(x) \) is:

\[
(f \circ g)(x) = 10x^2 + 35x + 70
\]

Let me know if you'd like further details or have any questions!

Here are 5 related questions to explore:
1. What is the domain of \( (f \circ g)(x) \)?
2. How would you find \( (g \circ f)(x) \)?
3. Can you compute \( f(g(2)) \) using the same method?
4. What happens if the functions were subtracted instead of composed: \( f(x) - g(x) \)?
5. How can you graph the polynomial \( 10x^2 + 35x + 70 \)?

**Tip:** When composing functions, always remember to substitute the inner function into every instance of the variable in the outer function.

Find (f ∘ g)(x) for f(x) = 5x + 5 and g(x) = 2x^2 + 7x + 13.

Learn how to find the composition of functions (f ∘ g)(x) for f(x) = 5x + 5 and g(x) = 2x^2 + 7x + 13. This example involves key concepts in algebra, including function composition and polynomial manipulation.

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