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 ..

One can view $f$ as a machine that takes an input (usually called $x$) and outputs something based on that input.
It is usually written in the general case as something like $f(x)=3x-5$ which says whatever our input $x$ happens to be, we output something that is (in this case) $3$ times that input and then subtract five.
In the above example it would be something like $f(\color{fuchsia}{1})=3\cdot \color{fuchsia}{1}-5$, or $f(\color{fuchsia}{2})=3\cdot \color{fuchsia}{2}-5$, or in general $f(\color{fuchsia}{x})=3\cdot \color{fuchsia}{x}-5$
In the case that the input happens to itself be written in a strange way, or even as a different function, that is okay.  It is still the input, and we manipulate it in exactly the same way.
$f(\color{fuchsia}{\frac{1}{x}})=3\cdot \color{fuchsia}{\frac{1}{x}}-5$ and $f(\color{fuchsia}{x+1})=3\cdot (\color{fuchsia}{x+1})-5$ for examples.
We may choose to reorganize things afterwards at our convenience.
For example: $f(\color{fuchsia}{2x+1})=3\cdot (\color{fuchsia}{2x+1})-5=6x+3-5=6x-2$
