How do you find the inverse of y = x/(x+1) and is it a function?
1 Answer
May 23, 2016
Explanation:
Isolate
y = x/(x+1) = ((x+1)-1)/(x+1) = 1-1/(x+1)
So, adding
1/(x+1) = 1-y
Taking reciprocals of both sides we get:
x+1 = 1/(1-y)
Subtracting
x = 1/(1-y)-1 = (1-(1-y))/(1-y) = y/(1-y)
This uniquely determines
So if
-
The domain of
f(x) is(-oo, -1) uu (-1, oo) -
The domain of
f^(-1)(y) is(-oo, 1) uu (1, oo)
So:
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The range of
f(x) is(-oo, 1) uu (1, oo) -
The range of
f^(-1)(y) is(-oo, -1) uu (-1, oo)