Finding the Inverse of a Function - Attempting to Solve

In summary, the conversation is about finding the inverse function and various methods to do so. The speaker suggests performing long division and swapping x and y, but is unsure of what to do next. They also mention that the inverse function can be expressed as x=f^{-1}(y) and can be plotted by rotating the original function's plot by 90 degrees.
  • #1
nod32
14
0

Homework Statement


JJDoR.png

Find the inverse

The Attempt at a Solution


Swapping x and y led me to nowhere. I'm really not sure where to go with this one, and a search online only led to simple problems where the previously mentioned method works.
 
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  • #2
Perform long division and then try swapping x and y again.
 
  • #3
I guess "inverse" means "inverse function". If [tex]y=f(x)[/tex] then [tex]x=f^{-1}(y)[/tex]. [tex]f^{-1}[/tex] is the inverse function. Can you express x in terms of y? You will have to solve some equation ...
If you plot your function with x horizontal and y vertical, and then rotate your plot by 90 degrees so that y is horizontal - you will see the plot of [tex]f^{-1}[/tex]. Now, calculate...
 
Last edited:

What is the inverse of a function?

The inverse of a function is a new function that undoes the action of the original function. It switches the input and output values of the original function.

How do you find the inverse of a function?

To find the inverse of a function, you can use the following steps:

  1. Replace f(x) with y.
  2. Switch the x and y variables.
  3. Solve for y.
  4. Replace y with f-1(x).
  5. The resulting function is the inverse of the original function.

What is the notation for the inverse of a function?

The inverse of a function is denoted as f-1(x), where the "-1" is a superscript and not an exponent.

Can every function have an inverse?

No, not every function has an inverse. For a function to have an inverse, it must be a one-to-one function, meaning each input has a unique output. Functions that fail the horizontal line test do not have an inverse.

What is the relationship between a function and its inverse?

The inverse of a function is the reflection of the original function over the line y=x. This means that the domain and range of the original function become the range and domain of the inverse function, respectively.

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