Let's find \( f \circ g \circ h \). Given: - \( f(x) = x - 8 \) - \( g(x) = \sqrt{x} \) - \( h(x) = x - 8 \) Step 1: Find \( g \circ h \): \[ g(h(x)) = g(x - 8) = \sqrt{x - 8} \] Step 2: Find \( f \circ (g \circ h) \): \[ f(g(h(x))) = f(\sqrt{x - 8}) = \sqrt{x - 8} - 8 \] **Final Answer:** \[ (f \circ g \circ h)(x) = \sqrt{x - 8} - 8 \]

Let's carefully find the composition \(f \circ g \circ h\), which means applying \(h\), then \(g\), then \(f\) to an input \(x\). The order of composition is from right to left: first \(h(x)\), then \(g\) on that result, then \(f\) on the result of \(g\). Given functions: - \(f(x) = x - 8\) - \(g(x) = \sqrt{x}\) - \(h(x) = x - 8\) --- ### Step 1: Find \(g \circ h\) This means \(g(h(x))\): \[ g(h(x)) = g(x - 8) = \sqrt{x - 8} \] --- ### Step 2: Find \(f \circ (g \circ h)\) This is \(f(g(h(x)))\): \[ f(g(h(x))) = f(\sqrt{x - 8}) = (\sqrt{x - 8}) - 8 \] --- ### **Final Result:** \[ \boxed{ (f \circ g \circ h)(x) = \sqrt{x - 8} - 8 } \] ### **Summary:** - First, input \(x\) into \(h\): \(h(x) = x - 8\). - Then, take that result and input into \(g\): \(g(h(x)) = \sqrt{x - 8}\). - Finally, input that into \(f\): \(f(g(h(x))) = \sqrt{x - 8} - 8\). This completes the step-by-step solution.