+0  
 
0
103
1
avatar

The function $h(x)$ is defined as: \[h(x) = \left\{ \begin{array}{cl} \lfloor 4x \rfloor & \text{if } x \le \pi, \\ 3-x & \text{if }\pi < x \le 5.2, \\ x^2& \text{if }5.2< x. \end{array}\right.\] Find $h(h(\sqrt{2}))$.

Guest Aug 27, 2017
Sort: 

1+0 Answers

 #1
avatar+78678 
+2

\(\[h(x) = \left\{ \begin{array}{cl} \lfloor 4x \rfloor & \text{if } x \le \pi, \\ 3-x & \text{if }\pi < x \le 5.2, \\ x^2& \text{if }5.2< x. \end{array}\right.\]\)

 

Find   \($h(h(\sqrt{2}))$\)

 

We want to first evaluate   h (√2)....note that   √2 < pi ....so  we want to use the first function

h (√2)   =    floor [ 4(√2) ]   =  floor  [ ≈ 5.657 ]  ....and we want the greatest integer < or  = to 5.657

This  is 5

 

Now ....we want to evaluate  h(5).....this falls between  pi   and 5.2, so we want to use the second function

 

So   h(5)  =  3 - 5   = -2

 

So.....to recap

 

h ( h(√2) )  = h (5)  =  -2

 

 

 

cool cool cool

CPhill  Aug 28, 2017
edited by CPhill  Aug 28, 2017
edited by CPhill  Aug 28, 2017

17 Online Users

avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details