Problem
Use the functions $f(x)=x^{2}-3 x-18$ and $g(x)=x^{2}+3 x-18$ to answer parts (a) through $(g)$. (a) Solve $f(x)=0$. (d) Solve $f(x)>0$. (g) Solve $f(x) \geq 1$. (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 set is $\{-3,6\}$. (Use a comma to separate answers as needed.) (b) The solution set is (Use a comma to separate answers as needed.) Clear all Check answer
Solution
Step 1 ：The first question asks to solve the equation \(f(x)=0\). This is a quadratic equation and can be solved using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a\), \(b\), and \(c\) are the coefficients of the quadratic equation \(ax^2 + bx + c = 0\). In this case, \(a=1\), \(b=-3\), and \(c=-18\).
Step 2 ：The solutions to the equation \(f(x)=0\) are \(x=-3\) and \(x=6\). These are the x-values where the function \(f(x)\) intersects the x-axis.
Step 3 ：Final Answer: The solution set is \(\boxed{-3, 6}\).
