look guys I reall need help, especially with math. you see, im in college. and I think I might have to drop out of math and take it again next semester. its 11:00pm here and I still have to finish these problems and START English. I pretty much do this everyday: I got to school, then I work for 2-3hrs, then I do homework until 1am to wake up at 6 and start a new day. I can't take it anymore.
so please, please help me out.
I need to find the inverse of y=3(x-2)^2 + 7[2,infinty)
so far I have (x-3)/3=Y^2 - 4y
Well, I'm gonna put here a few tips but not solve the homework for you.
Zeroth, refer to the definition of mathematical function. A function is a mathematical operator that changes values from input group into output group, correct? And each input value has it's own, singular corresponding output value. Two input values may share the same output value, though.
Inverted function does the same, except it is a mathematical operator that works backwards, changing the output values of the original function into their respective input values.
However, if multiple values from input group result in the same output value, there will be problem for the inverse function since it would need to produce multiple output values and that is not possible for the concept of (single) function. This kind of functions are not directly invertible and need to be split into two - or more - parts depending on how many values of x are produced out of value of y at different ranges.
Furthermore it is possible that you end up getting results out of imaginary range depending on what you need to do during the inversion operations, which define what values of variable y are acceptable for the inverse function.
Now that you remember what to keep in mind when looking at inverse functions...
First, look at the graph of the equation (the images aren't hosted very long so if you don't see the image, go to
wolfram alpha and input the equation there to see the graph).

At value x=2, function f(x)=y=7. Above and below this value of x, the function gets values larger than seven for y. However, if values of y are less than seven, there simply is no corresponding x-value, so your inverse function will only be valid when y>= 7, and even then there's basically two values of x that each value of y produces, which means that for a complete solution you will need complex numbers... and depending on your level you may or may not need to include them.
Anyway... multiple values of X at same Y means that the function is not directly invertible. A function means that it produces one output value out of one input value. If it produces more, then there is a problem and it means that for an inverted function you need to divide it into two or more parts depending on how many results you get at each value of y.
As for actually solving the equation into f(y)=x form rather than f(x)=y, it is largely a simple matter of conversion - just manipulate it as long as you need to so that you have single x at one side and a function with y- variables in it on the other side.
In this case, I'll give you a hint...
Sqrt ( f(x)^2 ) = | f(x) | (bars here mean absolute value, alternative marking would be abs f(x) or +-f(x) )
What then is Sqrt ( (x - 2)^2 ) ?
I need to find the inverse of y=(3x-4)/(2x+5)
Same approach.

First of all you'll see that when 2x+5 = 0 due to division by zero, the function does not have valid output (or, well, lim f(x) = +- infinity depending on which side you're approaching it from) and that needs to be taken into account, of course.
Regarding the solving of the equation... I would do
polynomial long division first:
3/2____2x + 5 | 3x - 4
-2x - 15/2 0x - 23/2
Therefore, 3x-4 / 2x+5 == 3/2 - 23/(2*(2x+5))...
y = 3/2 - 23 / 2(2x+5)
...and I believe you should be able to continue from that point.