“P or not-P, that is the question”
Well, given the starting point, we can find all the values for ascending odd inputs starting from 3:
f(3) = 5
f(x) = f(x-2) + 1
f(5) = f(5-2) + 1 = f(3) + 1 = 5 + 1 = 6
f(7) = f(7-2) + 1 = f(5) + 1 = 6 + 1 = 7
f(9) = f(9-2) + 1 = f(7) + 1 = 7 + 1 = 8
f(11) = f(11-2) + 1 = f(9) + 1 = 8 + 1 = 9
So are we allowed to assume that the function is continuous and linear? If so:
f(x) = x/2 + 7/2 = (x + 7)/2
f(4) = (4 + 7)/2 = 11/2 = 5.5
Glad other people are getting -12, the rest are autistic
Mate, I'm glad you got the right answer, but root of 4 = 2, thus 2-3 = -1, and -1^2 = 1
He's saying you're merely average, wank stain
>That's some assumption you're making there. Can you prove that's the case for all recursive functions of this type?
Not that guy. Also not sure how to prove it, but fairly certain that the only solutions to f(x) = f(x+a)+b are the linear functions with the appropriate slope.
What i did was read the info and comprehend it really.
It's more an issue of understanding than proving.
But i'll try to explain
f(x) = f(x-2) +1
This means that increasing x by 2, increases f(x) by 1
In other words
Divide both sides by two
Realize the first part is really f(4)-f(3)
Insert value for f(3)
You can take it from here
Fuck i accidentally proved it.
How do I get gud at math?
I mean math, not calculating things.
I've basically forgotten all of my A-Level knowledge from High school and I wanna go to University.
How do you learn math in an effective, fast way?
Getting the concepts and mechanism down, abstract concepts in a way you can understand it, ...
Maybe there is some math wizard (Math graduate) in here.
>yes but he can see it is linear because if x is increased by 2 f(x) is increased by one.
That doesn't make sense.
IF you assume a linear function, the answer is correct. I can give you a lot of other functions that fulfill the given criteria which are not correct.
For example, take a function periodic in 2 and add it to your linear solution.
f(x)=1/2*x + 3.5
is your solution
g(x)=1/2*x + 3.5 + sin(pi*(x-1) / 2)
is another one.
>Being this retarded
>Unable to do basic algebra
If the equation gives you the square root you assume it's positive unless stated otherwise.
If you introduce the root into the equation, then you have to account for both.
jesus christ youre that kid who aced math but not a social life.
The question is obviously not at the level in which you answered wether it was specified or not quit being a faggot trying to show off your highschool math skills you poofy little cunt
I m astounded by the fact that we're even discussing this, are /b/tards really this fucking stupid? (not refferring to your post, just in general and yes of course that's the answer)
Except it isn't, because that's -√a
I'll have you know I graduated magna cum loudly from Harvard 5 years ago and this is the sort of shit that would get you laughed at there. Maybe if you weren't so fucking stupid you'd understand.
So harvard never learnt + - signs
√4 = +-2
-√4 = + - 2
essentially you times the answer by a negative and flip the answers. Glad you graduated in taking cum at harvard maybe nextime focus on math and not jizz
Funfact: Americans are learning the math in college we already learn in germany in high school, but we cover it even there more deeply.
Burgers have in their 2nd year college the same level of math we had in grade 11. GG education
>(except pure math programs)
Let's see how clever you really are /b/.
Added constraint of boundary conditions of y=y'=1 at x=0.
√4 is only equal to a single value, which is 2. However, when you construct an algebraic expression, like "4=x^2", then x has two different solutions, which are 2 and -2. These values of x are not equal, otherwise any number would then be equal to it's negative counterpart, which would break arithmetic. For an example; 4-3=1. But 4 would then technically be equal to √16, which is then equal to -4. This would mean that 4-3=-7=1. But the algebraic expression "x=√16 -3 would have two solutions, being -7 and 1.
Is it really so hard to understand?
That's only true for the poorest of American schools for students who take the "normal" ciriculum, but at my high school most students were in the "advanced" courses and we learned college level calc 2 in junior year.
>square is always positive
>talks about 'many'
ok man ima break it down for you.
THE SQUARE ROOT OF X
has twwwwwwwwoo answers. Two seperate answers. Just because √4 = + or - 2
doesnt mean that -2= 2
it means that the two possible solutions are
ok harvard cum degree?
Multiple partial derivatives and all the extra tricks to solve complex integrals. Basic limits, derivatives, and integrals are calc1.
I went to public school, faggot. It just wasn't an innercity, nignog infested shithole.
all you fucking retards need to go back to school
The answer is 0
>4+3-5*2^2+2-(sqroot4 - 3)^2
As always, PEMDAS
Google it faggots
oh so you did high level highschool maths. Congratz man thats super unusual never seen anyone do that.
Your school must be ahead of other nations there buddy wow fuck me why even bother going to uni I think you should apply to NASA