If f(x) = 26 + 3

x + 13
 and g(x) = 2x2 + 5, compute the composition (f ∘ g)(3).

(f ∘ g)(3) 

To compute the composition \((f \circ g)(3)\), we need to evaluate \(g(3)\) first and then use that result as the input for \(f(x)\).

### Step 1: Compute \(g(3)\)

Given \(g(x) = 2x^2 + 5\), we can substitute \(x = 3\):

\[
g(3) = 2(3)^2 + 5
\]

Calculate \(3^2\):

\[
3^2 = 9
\]

So, 

\[
g(3) = 2 \times 9 + 5 = 18 + 5 = 23
\]

### Step 2: Compute \(f(g(3)) = f(23)\)

Given \(f(x) = \frac{26 + 3}{x + 13}\), substitute \(x = 23\):

\[
f(23) = \frac{26 + 3}{23 + 13}
\]

Simplify the expression:

\[
f(23) = \frac{29}{36}
\]

### Conclusion

Thus, the value of the composition \((f \circ g)(3)\) is:

\[
(f \circ g)(3) = \frac{29}{36}
\]

Would you like further details or have any questions?

Here are some related questions you might be interested in:
1. How do you find the composition of two functions in general?
2. What is the domain of the composite function \(f(g(x))\)?
3. How does the composition of functions relate to real-world applications?
4. Can a composite function ever be undefined?
5. What are some properties of composite functions?

**Tip:** When working with compositions of functions, always evaluate from the innermost function outward.

Learn how to compute the composition (f ∘ g)(3) using function composition and quadratic equation principles. Detailed step-by-step solution provided. Suitable for high school students.

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