# Thread: Find The forumula for the inverse of a given function

1. ## Find The forumula for the inverse of a given function

So one problem is f(x)=x^3 , In my head I know its x^(1/3) because
y=x^3
Then i think I Do the third square root to both sides to get that answer but am not sure.

This is the one where Im haveing the most trouble

f(x)=(3x+1)/(2x-5) So I Multipy each side by 2x-5 and get
y(2x-5) which factors into
2xy-5y=3x+1 and am not sure what to do from here

Any help would be greatly appreciated.

The answer in the back of the book is y=(5x+1)/(2x-3)
even with that I cant figure out how they came up with it

2. ## Re: Find The forumula for the inverse of a given function

transfer all terms with y to the right side and all x to the left and solve for x ...to be a function of y..the interchange the x with y and thats it...you must find
(5x+1)/(2x-3) as inverse to the original function

Good luck
Minoas

3. ## Re: Find The forumula for the inverse of a given function

I can help you to a certain extent, but the ONLY thing I myself am unsure of is why it's 5x+1 and not 5x-1, or -5x+1 conversely.

First, the easiest way to solve this would be to switch the x's and y's. Equation becomes

$\displaystyle x=\frac{3y+1}{2y+5}$.

You were correct to multiply the denominator, then you get

$\displaystyle x(2y+5)=3y+1$.

Distribute:

$\displaystyle 2xy+5x=3y+1$

Isolate all terms with y on one side, so I'll subtract 3y from the right and 5x from the left to keep the formatting of your books answer more intact:

$\displaystyle 2xy-3y=-5x+1$

Factor out a y

$\displaystyle y(2x-3)=-5x+1$ and divide by 2x-3

$\displaystyle y=(-5x+1)/(2x-3)$

Now you just have to hope that either your book is wrong or somebody can explain to you why it's 5x+1 without a negative.

Hope I helped at least a bit.

4. ## Re: Find The forumula for the inverse of a given function

It started out as f(x)=(3x+1)/(2x-5) I think you did f(x)=(3x+1)/(2x+5)

Thank you though i just couldn't wrap my head around it.
I Was failing at getting like terms on their own side I think.
I went through it again and got the correct Answer TYVM

Also where is the reference material for this site to make my math problems look like yours

5. ## Re: Find The forumula for the inverse of a given function

Oops, 2x-5 would indeed make a ton more sense as to why it's 5x+1 lol. Not sure why my mind read it as 2x+5.

And the way to format math problems like this is called LaTex, there's a specific sub-forum on this website with how to do it all. Everything goes inside [ tex][/tex] brackets.