ROOT FUNCTIONS Solving Radical Inequalities (Page 2 of 2)

We now interpret the inequality sqrt(2x-5)-2-sqrt(x-2) < 0 in terms of the function we have graphed. The solution set will be all values of x for which the function Y1 has negative y-values. Let's use TRACE to identify where these values of x are.

 TRACE key. Left arrow key....

 Right arrow key....

Calculator screen image. Calculator screen image.

Since the x-intercept has a y-value equal to 0, it is NOT part of the solution set. The x-values to the left of 27 yield negative y-values. The inequality sqrt(2x-5)-2-sqrt(x-2) < 0 means that the graph of Y1 must lie below the x-axis. Observing the graph, we see this is true if x is to the left of 27. We must also consider the domain of this function, which is x >= 2.5. The inequality is not defined for values of x less than 2.5. So, the solution set for the inequality is {x: 2.5 <= x <= 27}, or in interval notation, [2.5, 27).

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