## anonymous 4 years ago 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?

1. 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.

2. 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

3. anonymous

Do you have any idea about piecewise functions? I think you can create a piecewise function for this. Something like this maybe, $f(x) = \left\{\begin{array}{r} f(x) = 4, & x=4 \\f(x) = 3, & 4< x \leq 5 \\f(x) = -1, &x =-3,2\\ \end{array} \right.$

4. 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.

5. anonymous

Now, are we clear?

6. 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

7. anonymous

It will work, you need only graph it. |dw:1327387611159:dw|