Question

I'm looking for functions that satisfy each of these conditions. Hopefully there is some relation between these functions as well, but whatever we can find and is most general.

f(x)=-f(x)
f(x)=f(-x)
f(-x)=-f(x)

---
original question
f(x)≠-f(x)
f(x)≠f(-x)
f(-x)=-f(x)
---

f(x)=-f(x)
f(x)≠f(-x)
f(-x)≠-f(x)

f(x)≠-f(x)
f(x)≠f(-x)
f(-x)≠-f(x)

Answer 1

might want to state the domain and range

Answer 2

yes, kai

Answer 3

well u wanna a function
odd not even , also this condition f(x)≠-f(x)

why not :)

Answer 4

your function cannot be true if the domain includes 0

Answer 5

Well it seems like sin(x) could satisfy this.

Answer 6

no.

Answer 7

knot theory function

Answer 8

like I said, f(0)=f(-0)

Answer 9

yep , it does , kai

Answer 10

so not odd, or even
or sort of reflected

Answer 11

what the hell @ikram002p

Answer 12

sine is odd

Answer 13

so it satisfies f(x) = -f(-x)

Answer 14

such a function on the reals does not exist, because 0=-0

Answer 15

Then sin(x) with 0 removed from the domain will do it, yeah?

Answer 16

what is negative zero?

Answer 17

0

Answer 18

no.... is it?

Answer 19

-0=-1*0=0