SOLUTION: If f(x)=(x+2)/(x-3) a) Find a formula for f^-1 (please show work) b) Show algebraically, that they are inverses of each other. Thanks in advance for your time and assistan

Algebra ->  Rational-functions -> SOLUTION: If f(x)=(x+2)/(x-3) a) Find a formula for f^-1 (please show work) b) Show algebraically, that they are inverses of each other. Thanks in advance for your time and assistan      Log On


   

Question 753513: If f(x)=(x+2)/(x-3)
a) Find a formula for f^-1 (please show work)
b) Show algebraically, that they are inverses of each other.
Thanks in advance for your time and assistance.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The quick, crude way:

say f(x) is y, and switch places of x and y.
x=%28y%2B2%29%2F%28y-3%29
x%28y-3%29=y%2B2
xy-3x=y%2B2
xy-y=3x%2B2
y%28x-1%29=3x%2B2
y=%283x%2B2%29%2F%28x-1%29

This must be called something other than f(x). Say g(x) is the formula we just found. highlight%28g%28x%29=%283x%2B2%29%2F%28x-1%29%29 and this is the inverse of f(x).

Now if they are inverses, then you should form the compositions, f(g(x)) and g(f(x)) and both of them should be found to be x.