what is the relation between $f(x+1)$ and $f(x)$? I searched so much over math sites and google but I didn't find helpful hints and required knowledge or the specific name of this topic in function.
I stuck in relation and operations on $f(x)$ which is really important for solving problems.
for example  relation between $f(x)$ and $f(x+1)$
in more complicated form for instance:
1. $$f(x)=3x-5$$
$$f(2x+1)=?$$
true answer is $$2f(x)+8$$
I tried this solution but it doesn't work
$f(2)$*$f(x)$+$f(1)$=?
$f(1)$=$-2$
$f(2)$=$2*3-5=1$
$f(2)$*$f(x)$+$f(1)$=?
$1(3x-5)-2$=$3x-7$ which gives us $f(x)-2$
another instance:
$$f(-x)=2f(x)+6$$
$$f(3)=?$$
true answer is $$-6$$
I tried this solution 
$f(x)(-1)$=$2f(x)+6$
$-f(x)$=$2f(x)+6$
$-3f(x)$=$6$
$f(x)$=$-2$
so I will be really appreciative if you tell me the relation between operation on $f(x)$ like $f({1\over x})$ , $f(x-1)$  and ..

There are no general way of expressing $f(x+n)$ (or $f(nx)$ or $f(\frac{x}{n})$) in terms of $f(x)$. 
Functions satisfying $f(x+y)=f(x)+f(y)$ are called linear, and make a fairly small (however you want to define that) part of all functions, and make for a lot study. Similarily functions satisfying other "nice" equations can be studied.
What you call the "true answer" to the problem in the question is correct (other answers tell you how to see that), but a rather strange expression.
