Thread: Functions

OK, the problem i have here i can't even begin to solve, so im in need of some help. Here's the exact problem:

If the following conditions are true
1. f '(x) = f(x) - g(x) [the apostrophe means the derivitive of f of x]
2. g '(x) = g(x) - f(x)
3. f(0) = 5
4. g(0) = 1
5. f and g are continuous are differentiable functions

Find the constant value of f(x) + g(x) for all x. Explain your work and your steps.


There it is. I don't get it at all, but my math teacher thinks i should for whatever reason. Please help! Thanks in advance!

;

;

;

and

and

then we have and . So the constant value of You can use the two equations to check that all of the given equations hold for all .

Thanks a lot, i get most of what you said. But can you explain how you came up with the second part:

f(x)= f '(x) + g(x)

and how you used that to find out that f '(x) = 4

thats the one part i still dont get

Originally Posted by Blue Griffin

Thanks a lot, i get most of what you said. But can you explain how you came up with the second part:

f(x)= f '(x) + g(x)

I got this from the first equation you gave me . All I did was add on both sides. I did the same thing for the second equation you gave me to get . It is actually not even necessary to re-write it this way.

and how you used that to find out that f '(x) = 4

thats the one part i still dont get

how about i show you how to do it with JUST the 4 equations you gave me without any reordering. you are given:









Using this, you can solve for and :

and likewise

Now repeating my earlier argument, and likewise

Now, and likewise

So then and . Adding these two together yields . The constant you are looking for is .