Question 1088006: My question is about inverse functions, didn't see an area to submit them. Anyway I was hoping some one could help me with 2 questions that are confusing to me.
1). If g(x) and f(x) are inverse functions, then (gof)(x)= f(x),x,(fof)x)or (gog)(x). I think the answer is either f(x) or x.
2).what is the inverse function of f(x)=(x-1)/(x) ?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 1) (gof)(x) = f(x)
:
you can prove it by using an example
f(x) = x - 1
y = x - 1
x = y - 1
f^(-1)(x) = x + 1
:
g(x) = x + 2
y = x + 2
x = y + 2
g^(-1)(x) = x - 2
:
(g^(-1)of^(-1))(x) = x +1 - 2 = x - 1
***************************************************
2) f(x) = (x-1)/(x)
y = (x-1) / x
x = (y-1) / y
xy = y - 1
xy - y = -1
y(x-1) = -1
f^(-1)(x) = -1/(x-1)
***************************************************
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