Question

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?

Answer 1

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.

Answer 2

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

Answer 3

Do you have any idea about piecewise functions? I think you can create a piecewise function for this.

Something like this maybe,
\[f(x) = \left\{\begin{array}{r} f(x) = 4, & x=4 \\f(x) = 3, & 4< x \leq 5 \\f(x) = -1, &x =-3,2\\ \end{array} \right.\]

Answer 4

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.

Answer 5

Now, are we clear?

Answer 6

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

Answer 7

It will work, you need only graph it.