Use the functions $f(x)=-x^{2}+9$ and $g(x)=5 x+9$ to answer parts $(a)-(g)$.
(a) Solve $f(x)=0$.
(d) Solve $f(x)> 0$.
(g) Solve $f(x) \geq 9$.
(b) Solve $g(x)=0$.
(e) Solve $g(x) \leq 0$.
(c) Solve $f(x)=g(x)$.
(f) Solve $f(x)> g(x)$.
(a) The solution to $f(x)=0$ is $x=-3,3$.
(Type an integer or a fraction. Use a comma to separate answers as needed.)
(b) The solution to $g(x)=0$ is $x=-\frac{9}{5}$.
(Type an integer or a fraction. Use a comma to separate answers as needed.)
(c) The solution of $f(x)=g(x)$ is $x=$
(Type an integer or a fraction. Use a comma to separate answers as needed.)
\(\boxed{x = 0}\)
Step 1 :\(f(x) = -x^{2} + 9 = 0\)
Step 2 :\(x^{2} = 9\)
Step 3 :\(x = \pm3\)
Step 4 :\(\boxed{x = -3, 3}\)
Step 5 :\(g(x) = 5x + 9 = 0\)
Step 6 :\(x = -\frac{9}{5}\)
Step 7 :\(\boxed{x = -\frac{9}{5}}\)
Step 8 :\(f(x) = g(x)\)
Step 9 :\(-x^{2} + 9 = 5x + 9\)
Step 10 :\(x^{2} + 5x = 0\)
Step 11 :\(x(x + 5) = 0\)
Step 12 :\(\boxed{x = 0, -5}\)
Step 13 :\(f(x) > 0\)
Step 14 :\(-x^{2} + 9 > 0\)
Step 15 :\(x^{2} < 9\)
Step 16 :\(\boxed{-3 < x < 3}\)
Step 17 :\(g(x) \leq 0\)
Step 18 :\(5x + 9 \leq 0\)
Step 19 :\(x \leq -\frac{9}{5}\)
Step 20 :\(\boxed{x \leq -\frac{9}{5}}\)
Step 21 :\(f(x) > g(x)\)
Step 22 :\(-x^{2} + 9 > 5x + 9\)
Step 23 :\(x^{2} + 5x < 0\)
Step 24 :\(\boxed{-5 < x < 0}\)
Step 25 :\(f(x) \geq 9\)
Step 26 :\(-x^{2} + 9 \geq 9\)
Step 27 :\(x^{2} \leq 0\)
Step 28 :\(\boxed{x = 0}\)