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Question 349122: f(x)=1+(3/(x-2))
State the domain of f^-1(x)
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! f(x)=1+(3/(x-2))
State the domain of f^-1(x)
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First, find the inverse of:
f(x)=1+(3/(x-2))
.
Set f(x) to y:
y=1+(3/(x-2))
Switch x for y and y for x:
x=1+(3/(y-2))
Solve for y:
x(y-2)=(y-2)+3
xy-2x = y+1
-2x = y+1-xy
-2x-1 = y-xy
-2x-1 = y(1-x)
(-2x-1)/(1-x) = y
(2x+1)/(x-1) = y
.
Therefore:
f^-1(x) = (2x+1)/(x-1)
Domain specifies values x can take --
All numbers except x=1 (denominator can't be zero)
OR, it can be specified as
(-oo, 1) U (1, oo)
where oo indicates infinity
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