SOLUTION: f(x) = (x+3)/(x+6) f^(-1)(-1) =

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Question 976198: f(x) = (x+3)/(x+6)
f^(-1)(-1) =
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
if f%28x%29+=+%28x%2B3%29%2F%28x%2B6%29, to find f%5E%28-1%29%28-1%29 first find f(x) =
f%5E%28-1%29%28x%29
since f%28x%29=y, we have
y+=+%28x%2B3%29%2F%28x%2B6%29....swap x and y
x+=+%28y%2B3%29%2F%28y%2B6%29.......solve for y
x%28y%2B6%29+=+%28y%2B3%29

xy%2B6x+=+y%2B3
xy-y+=+-6x%2B3
%28x-1%29y+=+-3%282x-1%29
y+=+-3%282x-1%29%2F%28x-1%29
so, f%5E%28-1%29%28x%29=-3%282x-1%29%2F%28x-1%29
now find f%5E%28-1%29%28-1%29
f%5E%28-1%29%28-1%29=-3%282%28-1%29-1%29%2F%28-1-1%29
f%5E%28-1%29%28-1%29=-3%28-2-1%29%2F%28-2%29
f%5E%28-1%29%28-1%29=-3%28-3%29%2F%28-2%29
f%5E%28-1%29%28-1%29=9%2F%28-2%29
f%5E%28-1%29%28-1%29=-9%2F2
or, as decimal
f%5E%28-1%29%28-1%29=-4.5