1. We are asked to find the composition \((g \circ f)(x)\), which means we substitute \(f(x)\) into \(g(x)\). 2. Given functions: \[f(x) = 5x + 6\] \[g(x) = 2x^2 - x - 1\] 3. The composition \((g \circ f)(x) = g(f(x))\) means replace every \(x\) in \(g(x)\) with \(f(x)\): \[g(f(x)) = 2(f(x))^2 - f(x) - 1\] 4. Substitute \(f(x) = 5x + 6\): \[g(f(x)) = 2(5x + 6)^2 - (5x + 6) - 1\] 5. Expand \((5x + 6)^2\): \[(5x + 6)^2 = (5x)^2 + 2 \cdot 5x \cdot 6 + 6^2 = 25x^2 + 60x + 36\] 6. Substitute back: \[g(f(x)) = 2(25x^2 + 60x + 36) - 5x - 6 - 1\] 7. Distribute the 2: \[= 50x^2 + 120x + 72 - 5x - 6 - 1\] 8. Combine like terms: \[= 50x^2 + (120x - 5x) + (72 - 6 - 1) = 50x^2 + 115x + 65\] Final answer: \[(g \circ f)(x) = 50x^2 + 115x + 65\]