/sci/ - Science & Math

What is f(x) equal to?

>>10474623
(c)

>>10474649
Right. But how tf?

>>10474623
Let x=1 to see that f(1) = 1 and let x=-1 to see that f(-1) = -1.
Therefore 1 and -1 are in S. So the answers (a) and (b) can't be correct.

>>10474656
Change x to 1/x in the functional equation to get two linearly independent equations in the two variables f(x) and f(1/x). Solving for f(x) gives f(x) = 2/x - x. Set f(x) = f(-x) to get x = +/- sqrt(2).

>>10474670
f(x) should be f(-x) though

>>10474686
Thanks Anon.

let x be nonzero and in S. then

f(x) + 2f(1/x) = f(-x) + 2f(-1/x)

but lhs is 3x and rhs is -3x. we must have x = 0, a contradiction

>>10475411

>>10475431
what is wrong with what I said?

>>10475437
Think a bit more deeply about how you've incorrectly constructed your equation and get back to me.

Part of leaning is working through your easily avoided mistakes.

>>10474643
3x - 2f(1/x)

>>10475528
No. Just 3x - 2(1/x).

>>10475533
Lol, retard

>>10475411
Based retard.

>>10474623
f(x) + 2f(1/x) = 3x
2f(1/x) + 4f(x) = 6/x
3f(x) = 6/x - 3x
f(x) = 2/x - x
it is quite clear that this works
then 2/x - x = 2/(-x) + x implies 4/x = 2x implies x = +sqrt(2), x = -sqrt(2)
One can check very easily that both work, and so S has 2 elements.

>>10475411
>>10475437
what allows you to conclude that f(1/x) = f(-1/x)?

>>10476015
f(x) = f(-x) for all x,
so renaming variables to avoid confusion:
f(y) = f(-y) for all y
let y = 1/x:
f(1/x) = f(-1/x)

>>10476045
>f(x) = f(-x) for all x,
Retard

>>10476219
>can't read set-builder notation
>calls me a retard
turbotard

>>10476345
>he thinks the stipulated conditions result in a contradiction

>>10476586
So the answer is the empty set.

>>10476594
I commend you!

You've managed to be the only person in this thread-perhaps even on /sci-to get a 4-option multiple choice problem wrong twice and still have 3-options left from which to choose a correct answer.

Absolutely stellar!

>>10476594
The answer is (c).

>>10476594
the answer is c

>>10476345
Lmao, you're the one who not only can't read set builder notation, but also can't read english. f(x) = f(-x) for all x in R. Suppose x in R. Then f(x) = f(-x). Now, show me how you can conclude that f(1/x) = f(-1/x).

>>10475411
>>10476045
>>10476345
>>10476594
you don't deserve anything but the worst treatment for pontificating with such certainty about a subject you can't be assed to spend even 10 minutes googling to learn about

i'm saying this in the most sincere and unironic way i can: fucking kill yourself faggot

>>10476657
Because if x is in R, 1/x is in R (x =\= 0 according to the problem). I haven't been on /sci/ in a while, is this the new .9.. = 1 thread?

>>10476679
C'mon man, don't be hyperbolic. He's made several admittedly elementary mistakes; I'm sure he understands that by now. No need to tell him to kill himself, let him learn.

>>10476693
Let S denote the set of all elements in R for which the function f (x)=2/x-x satisfies the relation f (x)=f (-x). Is it also true that S constitutes the elements for which f (1/x)=f(-1/x)?

Work through this algebraically and you'll understand.

just try f(x) = x
or f(x) = 1
how many solutions do you get

>>10476712
Who are you replying to? What are you trying to prove?

>>10476721
To the OP, who else?

>>10476693
>if x is in R, 1/x is in R
Why do you think that, retard?

>>10476693
Oops, I thought R was the set. I meant S when I said R in
>>10476657

>>10476707
Ah yes, fuck, I misread the problem.

I am the true turbotard.

Why is this thread still getting bumped even though I answered it 24 hours ago?

>>10474623
b

Anon is studying for JEE

>>10477615
yes, yes you fucking are
>>10477635
no, i answered it you moron

>>10476013
I like your reasoning, but, for a mathlet, could you clarify that you inversely multiplied the equation by two for:
>2f(1/x) + 4f(x) = 6/x

>>10479459
Rude

>>10479459
>no, i answered it you moron
No you didn't stop lying

>>10479916
he took the top equation, and did x = 1/(x’), and that got him
f(1/(x’)) + 2*f(x’) = 3/(x’), and because labels dont matter, this could be expressed as f(1/x) + 2*f(x) = 3/x, and then he multiplied both sides by 2.