SOLUTION: Find the inverse of the function g(x)=(x+3)/(4-x). What is the domain of g^-1(x)? What is the range of g(x)? PLEASE HELPP!!!!!!

Algebra ->  Inverses -> SOLUTION: Find the inverse of the function g(x)=(x+3)/(4-x). What is the domain of g^-1(x)? What is the range of g(x)? PLEASE HELPP!!!!!!      Log On


   

Question 841019: Find the inverse of the function g(x)=(x+3)/(4-x). What is the domain of g^-1(x)? What is the range of g(x)? PLEASE HELPP!!!!!!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Switch to x,y notation.
y=%28x%2B3%29%2F%284-x%29
Interchange x and y.
x=%28y%2B3%29%2F%284-y%29
Solve for y
x%284-y%29=y%2B3
4x-xy=y%2B3
y-xy=4x-3
y%281-x%29=4x-3
y=%284x-3%29%2F%281-x%29
This new y is the inverse of the original function.
Domain : All values except x=1
Range : All values.