Inverse of function and its domain/range?

In summary, the conversation is about finding the inverse of a given function and determining the domain and range for both the original function and its inverse. The given function is f(x)= (3x+4)/(5-2x) and the inverse is f^-1(x) = (5y-4)/(3+2y). The domain for f(x) is x ≠ 5/2 and the range is y ≠ 3/2, both of which are in the set of all real numbers. The inverse function has a domain of all real numbers and a range of all real numbers as well. The conversation also includes a question about evaluating the limit and discussing the domain and range in that context.
  • #1
adelaide87
24
0

Homework Statement



a) find the inverse of f(x)= (3x+4)/(5-2x)
b) state the domain anr rage for both f and f^-1


Homework Equations





The Attempt at a Solution



for f(x)
Domain:x ≠ 5/2, x ∈ R
Range: y ≠ 3/2, y ∈ R

Inverse (my answer):

f^-1(x) = (5y-4)/(3+2y)

I want to check and see if this is correct, and also get some guidance of the domain/range for the inverse?

Thanks!
 
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  • #2
how did you get that 3/2 is not in the range?

what about f(0.5833333333)?

f^-1 looks right though.
 
Last edited:
  • #3
I evaluated the limit from x > inf and a > -infWhen you do that, the result becomes -3/2

(sorry, just realized it wasnt -'ive above. Should be -3/2!)
 
  • #4
but shouldn't that be missing from the domain of f^-1 ?
The range of f is all of R and the range of f^-1 is also all of R

right?
 
  • #5
What I've put above is just the domain and range for f(x)

Domain:x ≠ 5/2, x ∈ R
Range: y ≠ -3/2, y ∈ R

--------------------------------------------------------

Its the inverse, f^-1(x), that I need help finding the domain and range for now.
 

What is the inverse of a function?

The inverse of a function is a function that undoes the original function's actions. It is like a "reverse" function that can take the output of the original function and give back the input.

How is the inverse of a function represented?

The inverse of a function is typically represented by adding a negative exponent to the original function's name. For example, if the original function is f(x), the inverse function would be written as f-1(x).

What is the domain of the inverse of a function?

The domain of the inverse of a function is the range of the original function. In other words, it is the set of all possible input values that the inverse function can take.

What is the range of the inverse of a function?

The range of the inverse of a function is the domain of the original function. This is because the output values of the original function become the input values of the inverse function.

How do you find the domain and range of the inverse of a function?

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

  1. Write the inverse function as f-1(x).
  2. Switch the x and y variables in the function.
  3. Solve for y.
  4. The resulting equation will be the inverse function in terms of x.
  5. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function.

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