Evaluate Expression Composition
1. Problem: Evaluate the expression $$\frac{22^2 + 22 - 12}{22 + 8}$$ and find the composite function $f \circ g(3)$ given \(g(x) = x^2\) and \(f(x) = 2x + 1\).
2. Simplify the numerator:
$$22^2 = 484$$
$$484 + 22 = 506$$
$$506 - 12 = 494$$
3. Simplify the denominator:
$$22 + 8 = 30$$
4. Evaluate the fraction:
$$\frac{494}{30} = \frac{247}{15}$$ (This fraction cannot be simplified further.)
5. Evaluate $g(3)$:
$$g(3) = 3^2 = 9$$
6. Evaluate $f(g(3)) = f(9)$:
$$f(9) = 2 \times 9 + 1 = 18 + 1 = 19$$
Final answers:
\[
\frac{22^2 + 22 - 12}{22 + 8} = \frac{247}{15}, \quad f \circ g(3) = 19
\]