Is this alternative odd function equation valid? An odd function is a function where: 
$$f(-x) = -f(x)$$
Is this alternative form valid ? 
$$f(x) = -f(-x)$$ 
I'm asking because an odd function graphically is symmetrical with respects to the origin. 
Which means that the x and y point's signs are flipped. 
The second form seems easier to read (assuming it's valid).
 A: (CW; just ensuring this question registers as answered.)
Yes: As remarked in the comments, the two equations are equivalent. This can be seen by simply multiplying both sides of one equation by $-1$ to obtain the other equation.
As to which one "seems easier to read," this is -- of course -- a matter of taste.
A: Yes, as long as $(-1)^2=1$. You have:
$$f(-x) = -f(x) \Rightarrow (-1)f(-x) = (-1)(-f(x)) \Rightarrow -f(-x) = (-1)(-1)f(x) = f(x) \Rightarrow f(x) = -f(-x)$$
and of course the reverse:
$$f(x) = -f(-x) \Rightarrow (-1)f(x) = (-1)(-1)f(-x) \Rightarrow -f(x) = f(-x) \Rightarrow f(-x) = -f(x)$$

While what seems easier to read is a matter of taste they generalize differently. If you replace negation with another operation(*) they will no longer be the same - not that it matters in your context, in another context one of the definitions might be more natural than the other.
(*) For example homogenity is a stronger condition which is defined as $cf(x) = f(cx)$ for any constant $c$ (not only $-1$). Here you see it might be more "natural" to define oddness with the first definition.
