Find Inverse of Function: Homework Help

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In summary: I can't believe I forgot simple algebra. Thanks.What I did was, multiply the numerator and then expand everything. Bring all the x-terms and the xy-terms to one side, and the y-terms and constants to the other. Then I factored out x, and divided by the other stuff!
  • #1
GHealy
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Homework Statement


I need to pass a test to get into college calculus, but there's a few things I've forgotten since may, one of them being how to find the inverse of a function with x in the denominator. I think I remember it being something really simple that I'm overlooking, but here it goes:

Homework Equations


f(x) = (x + 2)/(3x + 5)

1) y = (x + 2)/(3x + 5)
2) x = (y + 2)/(3y + 5)
3) this is where it starts to go crazy.

The Attempt at a Solution


My attempts were kind of convulsive, but I hope it'll suffice to say that I know to switch y with x, then solve the problem for y, which will be the inverse. I just don't know how to get y out of the denominator without getting a really complicated answer. (edit: I put what I was saying into math form above)

Thanks, if anyone knows this. I've done some re-learning in the past week or so; there are just a few things left that are too specific to find online.
 
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  • #2
Your goal is to use properties of equality of real numbers to find a formula for y. Either you can find a result or you cannot. Can you obtain an inverse in that general manner?
In fact, a result is possible; whether the result is a function, I leave for you to decide.
 
  • #3
If the [tex]y=\frac{x + 2}{3x + 5}[/tex] then x+2=y(3x+5). Your goal is to present x in terms of y. Now can you proceed?
 
  • #4
Дьявол said:
If the [tex]y=\frac{x + 2}{3x + 5}[/tex] then x+2=y(3x+5). Your goal is to present x in terms of y. Now can you proceed?

That's where I get, but I can't go further without jumbling the whole thing up.
 
  • #5
GHealy said:
That's where I get, but I can't go further without jumbling the whole thing up.

Distribute the y on the right hand side, separate y and non-y terms to opposite sides, factor out y and divide.

--Elucidus
 
  • #6
Elucidus said:
Distribute the y on the right hand side, separate y and non-y terms to opposite sides, factor out y and divide.

--Elucidus

*facepalm*

I can't believe I forgot simple algebra. Thanks.
 
  • #7
What I did was, multiply the numerator and then expand everything. Bring all the x-terms and the xy-terms to one side, and the y-terms and constants to the other. Then I factored out x, and divided by the other stuff!
Good luck =)
 
Last edited:

FAQ: Find Inverse of Function: Homework Help

What is the purpose of finding the inverse of a function?

The inverse of a function is used to reverse the effect of the original function. It allows us to find the input (x) value that corresponds to a given output (y) value. This is useful in solving equations and understanding the relationship between variables in a function.

How do I find the inverse of a function?

To find the inverse of a function, you can follow these steps:

  1. Write the function in the form y = f(x)
  2. Switch the x and y variables, so that the function is now x = f(y)
  3. Solve for y in terms of x
  4. The resulting equation is the inverse of the original function

Why is it important to check the inverse of a function?

It is important to check the inverse of a function because it is possible to make mistakes when finding the inverse. Checking the inverse ensures that the original function and the inverse function are truly inverses of each other. This is done by plugging in the inverse function into the original function and vice versa, and making sure that the resulting equations are equal to the input value.

Can all functions have inverses?

No, not all functions have inverses. For a function to have an inverse, it must be a one-to-one function, meaning that each input has a unique output. This can be determined by graphing the function and using the horizontal line test. If any horizontal line intersects the graph in more than one point, then the function is not one-to-one and does not have an inverse.

What is the difference between the inverse and the reciprocal of a function?

The inverse of a function is a way to reverse the effect of the original function, while the reciprocal of a function is a way to flip the function over the line y=x. The inverse of a function is a new function that can be found by following specific steps, while the reciprocal of a function can be found by simply taking the reciprocal of the function's output. However, not all functions have reciprocals, but they can still have inverses if they are one-to-one functions.

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