Example Solving Equations and Inequalities using Given Graphs

Solve the equations and inequalities using the given graphs.

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