Subjects algebra

Evaluate Expression Composition

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

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: \[ \frac{22^2 + 22 - 12}{22 + 8} = \frac{247}{15}, \quad f \circ g(3) = 19 \]