Inverse of function and its domain/range?

[adelaide87]

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!

 

[ocohen]

how did you get that 3/2 is not in the range?

what about f(0.5833333333)?

f^-1 looks right though.

 

[adelaide87]

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!)

 

[ocohen]

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?

 

[adelaide87]

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

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