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The problem asks for \((f \circ g)(x)\), which represents the composition of functions \(f(x)\) and \(g(x)\). This means we need to substitute \(g(x)\) into \(f(x)\).

Given:
- \(f(x) = 5x + 5\)
- \(g(x) = 5x^2 + 5x\)

We want to compute \(f(g(x))\), which means substituting \(g(x)\) into \(f(x)\):

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

Now, simplify:

\[
f(g(x)) = 5(5x^2 + 5x) + 5 = 25x^2 + 25x + 5
\]

Thus, the simplified expression for \((f \circ g)(x)\) is:

\[
(f \circ g)(x) = 25x^2 + 25x + 5
\]

Would you like any further details or clarifications?

Here are some related questions:
1. How do you compute the composition of two functions?
2. Can the composition of two functions ever be commutative?
3. What happens if we reverse the composition, i.e., find \((g \circ f)(x)\)?
4. How do you check if two functions are inverses using composition?
5. What is the domain of the composition of two functions?

**Tip:** When simplifying expressions in function compositions, always make sure to carefully substitute and apply distributive properties correctly!

Let f(x) = 5x + 5 and g(x) = 5x^2 + 5x. Find (f ∘ g)(x).

Learn how to find the composition of functions f(x) = 5x + 5 and g(x) = 5x^2 + 5x by substituting and simplifying to get (f ∘ g)(x) = 25x^2 + 25x + 5. This problem explores function composition and algebraic manipulation, suitable for Grades 9-11.

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