Finding the Inverse of f(x) = (2x-5)/(7x+4)

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In summary, the conversation is about finding the inverse of a function, specifically f(x)=(2x-5)/(7x+4). The attempt at a solution involves rearranging the equation to solve for y, with suggestions to multiply both sides by 7y+4 and collect terms with y on one side. The conversation also includes apologies for any rude comments made.
  • #1
luznyr
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Homework Statement



Find inverse of f(x) when f(x) = (2x-5)/(7x+4)

Homework Equations



none

The Attempt at a Solution



x=(2y-5)/(7y+4) and then i get stuck trying to rearrange back to y=...
 
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  • #2
Where do you get stuck?? Multiply both sides by 7y+4, move all of the terms with a y in them to one side and solve for y. It's not that hard.
 
  • #3
ok that gives x(7y+4) -2y= -5, 7xy+4x-2y=-5, so how do i get it back to y= then genius?
 
  • #4
Keep all your terms with 'y' in them on one side, and all the other terms on the other, and then take out a factor of 'y', and it should be clear from there.
 
  • #5
So 4x+5=2y-7xy=y(2-7x). Can you solve for y now, genius?
 
  • #6
haha yep ty
 
  • #7
BTW sorry about the 'it's not that hard' crack. If you don't see it, you don't see it.
 
  • #8
yeah sry bout the genius thing, thanks for the help anyone, much appreciated
 

FAQ: Finding the Inverse of f(x) = (2x-5)/(7x+4)

What is the inverse of the given function?

The inverse of f(x) = (2x-5)/(7x+4) is g(x) = (5-2x)/(7x).

How do you find the inverse of a rational function?

To find the inverse of a rational function, interchange the positions of x and y and solve for y. This will give you the inverse function of the original function.

Is the inverse of a rational function always a rational function?

No, the inverse of a rational function may not always be a rational function. It depends on the original function and its domain and range.

How do you graph the inverse of a rational function?

To graph the inverse of a rational function, you can graph the original function and then reflect it over the line y = x. This will give you the graph of the inverse function.

Can a function have more than one inverse?

No, a function can only have one inverse. If there are multiple outputs for a single input, then it is not considered a function and therefore cannot have an inverse.

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