Alright, I'm trying to teach myself Calculus. It's an interesting development. But I guess I'm missing some mathematical background or I have the worst memory in the universe.

Here are a couple problems I'm having with the introductory topic in my Calculus book I bought for myself to learn from:

1. If f(x)=x-1/x show that a) f(-x)=-f(x), (b) f(1/x)=-f(x).

2. Let g(x)=x^3. Show that g(-x)=-g(x).

This one's kind of the same problem but yeah.

3. Let g(x)=x^4+2x^2+1. Show that g(x)=g(-x).

4. We learn that in trigonometry that sin x (3 bar symbol)sin(pi-x). Hence f(sin x)=f sin[pi-x]). Now let f(x)=x sin x. Then x sin x = (pi-x), or x=pi-x. Hence pi=2x and since x is any value we choose, so is pi. What is wrong?

I don't know why, but I don't understand certain parts of a problem. It's like steps are missing in my head. And the textbooks are unforgiving in their explanations because it seems like the parts I'm missing in my head never appear in textbooks, no matter how many prior ones I refer to so I can try to gain an understanding of what I'm missing. I must either be looking in all the wrong places or I have some missing link in my brain. It might be that I have a big problem trying to understand what they're exactly saying, because they're not clear enough for me. I don't know. Help?