00:02
All right, so here's a function.
00:04
We want to prove that it is odd.
00:06
So remember that for an odd function, f of the opposite of x is equal to the opposite of f of x.
00:13
So we're going to find f of the opposite of x and show that it is equal to the opposite of what we're given here.
00:20
So f of the opposite of x is what we get when we substitute the opposite of x everywhere we have an x.
00:27
So we're going to have 1 minus e to the 1 over the opposite of x power over.
00:33
1 plus e to the 1 over the opposite of x power.
00:37
Now our job is to simplify, simplify, simplify until we get it to look like we want it or need it to look.
00:44
Okay, so the next step is going to be to change these exponents.
00:48
So when you see 1 over the opposite of x, that's the same as the opposite of 1 over x.
00:56
Okay, you can have that negative sign in the front instead of in the denominator.
00:59
So what we have here is 1 minus e to the negative 1 over x over 1 plus e to the negative 1 over x.
01:11
Now remember that a negative exponent is a reciprocal.
01:14
So this is equivalent to 1 minus 1 over e to the 1 over x over 1 plus 1 over e to the 1 over x...