If $f(x)=3x-4$ and $g(x)=\sqrt{x+5}$ (with domain $x\ge -5$), find the value of $(f\circ g)(9)$.\n\nA) $3\sqrt{14}-4$\nB) $3\sqrt{9}+4$\nC) $3\sqrt{14}+4$\nD) $3\sqrt{5}-4$

Step-by-step solution

1. Recall that $(f\circ g)(x)=f(g(x))$, i.e., apply $g$ first, then $f$.
2. Compute $g(9)=\sqrt{9+5}=\sqrt{14}$ (the argument $9$ satisfies $9\ge -5$).
3. Now apply $f$ to this result: $f(g(9))=f(\sqrt{14})=3\sqrt{14}-4$.
4. Thus $(f\circ g)(9)=3\sqrt{14}-4$, which matches option A.

Concept tested: Composition of functions

Published 12 September 2026 · How this solution was prepared and checked