Can you explain to me which functions are odd? f(x)=-1/2x^4+5 f(x)=-8x^3+5x f(x)=-4/x^3-x+1 f(x)=x^5/x^4-1 f(x)=-sqrt2x f(x)=3sqrtx -x^3 you!

A function is odd if f(-x)=-f(x).
So given a function, to check whether it is odd or not, we calculate f(-x). If it is equal to -f(x), then the function is odd; if not, it is not odd.





thus the function is not odd





thus the function is odd





thus the function is not odd





thus the function is odd





In this particular case f(x) and f(-x) can both exist only for x=0 (because one of them is certainly negative). Thus the function is not odd



similarly to the previous case,  the Domain of f is [0, infinity) and f(-x) cannot be calculated except for x=0. So the function is not odd.