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The given functions are:

\[
f(x) = 2x + 1, \quad g(x) = x^2 + 4, \quad \text{and} \quad h(x) = \frac{1}{x + 1}.
\]

You are asked to find \( (f \circ h \circ g)(x) \), which is the composition of these functions.

This composition is calculated as follows:

\[
(f \circ h \circ g)(x) = f(h(g(x))).
\]

Let's break it down step by step:

1. **Start with \( g(x) \):**
   \[
   g(x) = x^2 + 4.
   \]

2. **Next, substitute \( g(x) \) into \( h(x) \):**
   \[
  

Learn how to compute the composite function (f ◦ h ◦ g)(x) involving the functions f(x) = 2x + 1, g(x) = x^2 + 4, and h(x) = 1 / (x + 1). This problem explores function composition in algebra, suitable for advanced high school students.

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