For odd function f(-x)= -f(x)
1) f(-x)= sin(-x) = -sin(x)=-f(x) sin is odd function
2) f(-x) = sin(-2x) = -sin 2x=-f(x)
3) f(-x)= (-x)³+1 = -x³ +1 (not an odd function)
To be an odd function, it should be like this:
if a function is (x³+1), to be odd f(-x) should be -(x³+1)=-x³-1
4) f(x)= x/(x²+1)
f(-x) = (-x)/((-x)²+1)= -x/(x²+1)=-f(x)
So, f(-x) gives
,
that means that f(x)= x/(x²+1) is an odd function.
5)f(x) = ∛(2x)
f(-x) = ∛(2*(-x)=∛(2x*(-1)) = ∛(2x)*∛(-1)=- ∛(2x)= -f(x)
1) f(-x)= sin(-x) = -sin(x)=-f(x) sin is odd function
2) f(-x) = sin(-2x) = -sin 2x=-f(x)
3) f(-x)= (-x)³+1 = -x³ +1 (not an odd function)
To be an odd function, it should be like this:
if a function is (x³+1), to be odd f(-x) should be -(x³+1)=-x³-1
4) f(x)= x/(x²+1)
f(-x) = (-x)/((-x)²+1)= -x/(x²+1)=-f(x)
So, f(-x) gives
that means that f(x)= x/(x²+1) is an odd function.
5)f(x) = ∛(2x)
f(-x) = ∛(2*(-x)=∛(2x*(-1)) = ∛(2x)*∛(-1)=- ∛(2x)= -f(x)