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# Why can f(x)-17 have no inverse? watch

1. (Original post by _gcx)
Bit late to the party, but for the sake of aesthetics, you can write this as,

From which you can observe the function as being many to one through the periodicity of .
woah, what's this csc? i feel a bit stupid since im doing uni level and i still don't get it
2. (Original post by will'o'wisp2)
woah, what's this csc? i feel a bit stupid since im doing uni level and i still don't get it
it's just , sorry if that was unclear
3. (Original post by _gcx)
it's just , sorry if that was unclear
Ah right, so it's a sin graph with the function of the stuff int he brackets then?
4. (Original post by _gcx)
No, I intended it to be read as . My approach is more heuristic so if you're still confused, investigating turning points per the other posts is probably the way to go.
I personally don't see how you could easily tell that a function in the form is necessarily many to one. Could you elaborate?
5. (Original post by I hate maths)
I personally don't see how you could easily tell that a function in the form is necessarily many to one. Could you elaborate?
Looking back, I have no idea where I was going with that either, I probably wasn't paying much attention. I've added,

Edit: I have no idea where I was going with this. I should've really explained why the second term is not one-to-one, ie. is not one-to-one as its derivative is neither strictly positive nor strictly negative, then perhaps using the product rule to conclude that the function is not one-to-one.

Basically, a continuous function is one-to-one if its derivative is strictly positive or strictly negative.
6. (Original post by _gcx)
Basically, a continuous function is one-to-one if its derivative is strictly positive or strictly negative.
A continuous function need not have a derivative.
7. (Original post by Zacken)
A continuous function need not have a derivative.
Indeed, should I say, a continuous, differentiable function.
8. (Original post by _gcx)
Indeed, should I say, a continuous, differentiable function.
If a function is differentiable, it is automatically continuous - so there is no need to specify continuity.

NB: there wasn't anything technically wrong with your statement -- it just read weirdly because of the aforementioned.

[Also, you have sufficiency but not necessity, for example x^3 is differentiable and bijective, but has 0 derivative at 0]

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Updated: October 7, 2017
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