Example Solving Equations and Inequalities using Given Graphs

Solve the equations and inequalities using the given graphs.

1. Sove the equation $f(x)=g(x)$.
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   $f(x)=g(x)$ means that their $y$ values are equal. So, we need to find the intersecting points of those two functions. From the graphs, we can find that $f(x)$ and $g(x)$ are intersecting at $(-3, 1)$ and $(5, 5)$. Therefore, the solutions of the equation $f(x)=g(x)$ are $x=-3, 5$.
2. Solve the inequality $f(x) \geq h(x)$.
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   $f(x) \geq h(x)$ means that the graph of $f(x)$ is above or intersecting the graph of $h(x)$. From the graphs, we can find the graph of $f(x)$ is above the graph of $h(x)$ when $x>-7$ and is intersecting the graph of $h(x)$ when $x=-7$. So, the solution of the inequality $f(x) \geq h(x)$ is $[-7, \infty)$ or $\{x|x \geq -7\}$.
   
3. Solve the inequality [latex]g(x)Show Answer
   [latex]g(x)