SOLUTION: For the function f(x) = (1-x)/x , use composition of functions to show that f –^1 (x) = 1/(x+1) is its inverse. I will apreciate the help guys

The red graph below is the graph of .
The green dotted line is the graph of the identity function 



The inverse function f-1 is the reflection of the graph
of f(x) in or across the identity line whose equation is I(x)=x, which
is the green dotted line above.

Let's draw the graph of  f-1 =  (in blue) to see it it looks like
it really it is the reflections of the red graph f(x) in or across the identity
function, which is the green dotted line I(x)=x:



Yes it does look like it is.  To show this algebraically we must find the
composition f∘-1 and also the composition  f-1∘f(x) and show that in both cases 
we get the right side of the identity function I(x)=x, which is x.

f∘f-1(x) = 

Multiply top and bottom by LCD of (x+1)

f∘f-1(x) = 

f∘f-1(x) = 

f∘f-1(x) = 

So it gives x, which is the right side of the identity function I(x)=x,
which is the green dotted line.

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But we also have to show that it refects into I(x)=x both ways.

f-1∘f(x) = 

Multiply top and bottom by LCD of x

f-1∘f(x) = 

f-1∘f(x) = 

f-1∘f(x) = 

We have found that both f∘f-1(x) and f-1∘f(x) are equal to the right side 
of the identity function I(x) = x, and that proves that each is the reflection
of the other in the green dotted line which is the identity function I(x) = x,
because composition with each other gives the right side of I(x) = x, which is
just x.

Edwin