SOLUTION: find a formula for {{{f^(-1)(x)}}}. give the domain of {{{f^(-1)}}}, including any restrictioons "inherited" from f. {{{f(x)=(x+3)/(x-2)}}}

Algebra ->  Functions -> SOLUTION: find a formula for {{{f^(-1)(x)}}}. give the domain of {{{f^(-1)}}}, including any restrictioons "inherited" from f. {{{f(x)=(x+3)/(x-2)}}}       Log On


   

Question 348441: find a formula for f%5E%28-1%29%28x%29. give the domain of f%5E%28-1%29, including any restrictioons "inherited" from f.
f%28x%29=%28x%2B3%29%2F%28x-2%29

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28x%2B3%29%2F%28x-2%29
The domain if f(x) is 

%22%28%22infinity%22%2C%22%222%29%22U%22%282%2C%22infinity%22%29%22





Replace f(x) for y

y=%28x%2B3%29%2F%28x-2%29

Interchange x and y:

x=%28y%2B3%29%2F%28y-2%29

Solve for y

x%28y-2%29=y%2B3

xy-2x=y%2B3

xy-y=2x%2B3

y%28x-1%29=2x%2B3

y=%282x%2B3%29%2F%28x-1%29

chnage y to f-1(x)

f%5E%28-1%29%28x%29=%282x%2B3%29%2F%28x-1%29

The domain is %22%28%22infinity%22%2C%22%221%29%22U%22%281%2C%22infinity%22%29%22 

The green graph is the inverse.



Notice that the inverse f-1(x) is the reflection of f(x) 
across the identity line, the line whose equation is y=x, a line through
the origin that bisects to 1st and 3rd quadrants, the dotted line below:



Edwin