1. **State the problem:** We need to find $f(g(4))$ given the functions $f(x) = 2x + 7$ and $g(x) = x^2 - 1$. 2. **Understand the composition:** $f(g(4))$ means we first find $g(4)$, then plug that result into $f(x)$. 3. **Calculate $g(4)$:** $$g(4) = 4^2 - 1 = 16 - 1 = 15$$ 4. **Substitute $g(4)$ into $f(x)$:** $$f(g(4)) = f(15) = 2(15) + 7 = 30 + 7 = 37$$ 5. **Final answer:** $$f(g(4)) = 37$$