anonymous
  • anonymous
construct a function F(x) with the following 5 properties: 1. the domain of f(x) is [-3,2]U[3,5) 2. f(4) = 4 3. f(2) - f(-3) =0 4. f(x) <= 4 for 4<=x<=5 5. f(-3) < 0 any ideas?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Creating a Function is entirely up to you, you can introduce anything you like. For Example, \(f(x) = x, x \in [-3,2] \cup [3,5)\) \[\]Now in this function you couldn't say anything to me, it's my function and I have the right to restrict to any kind of domain I want. The only thing you need to worry about while creating a function is that you don't ignore the basic definition of the function i.e no element in domain can have more than 1 image in range.
anonymous
  • anonymous
it needs to include all the properties listed, so it can't be anything wanted. All of those properties go into figuring out the equation
anonymous
  • anonymous
Do you have any idea about piecewise functions? I think you can create a piecewise function for this. Something like this maybe, \[f(x) = \left\{\begin{array}{r} f(x) = 4, & x=4 \\f(x) = 3, & 4< x \leq 5 \\f(x) = -1, &x =-3,2\\ \end{array} \right.\]

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anonymous
  • anonymous
Now you don't have the right to question my function, I can bend it anyhow I want. Also in your problem no condition mentions that the function should be continuous or differentiable. So, I created a discontinuous function as they are easy to formulate.
anonymous
  • anonymous
Now, are we clear?
anonymous
  • anonymous
well i have to be able to graph this function, so i think that it needs to be a more conventional function a piece wise might work but not the way you have written it
anonymous
  • anonymous
It will work, you need only graph it. |dw:1327387611159:dw|

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