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The function h(x) is defined as:h(x) = \left\{ \begin{array}{cl} \lfloor 4x \rfloor & \text{if } x \le \pi, <br /> 3-x & \text{if }\pi < x \le 5.2, <br />...Find h(h(\sqrt{2})).

 Jan 8, 2015

Best Answer 

 #1
avatar+104963 
+5

OK....this seems a little confusing....but it's not too bad....

First, we need to see that x= √2 ≤ pi.....so this tells us that we should use the first piecewise function to evaluate h(√2)..so we have

h(√2) = floor (4√2) = 5

Now.....we want to put this result back into h(x)...but note....now we must use the piecewise function 3 - x since the "x" we're putting into h lies between pi and 5.2

So we have

f(5)  = 3 - 5  = -2

So h(h(√2)) just evaluates to -2

 

 Jan 8, 2015
 #1
avatar+104963 
+5
Best Answer

OK....this seems a little confusing....but it's not too bad....

First, we need to see that x= √2 ≤ pi.....so this tells us that we should use the first piecewise function to evaluate h(√2)..so we have

h(√2) = floor (4√2) = 5

Now.....we want to put this result back into h(x)...but note....now we must use the piecewise function 3 - x since the "x" we're putting into h lies between pi and 5.2

So we have

f(5)  = 3 - 5  = -2

So h(h(√2)) just evaluates to -2

 

CPhill Jan 8, 2015

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