SOLUTION: Verify algebraically, that (Fof^-1)(x)=x for f(x)=1/(2x+4)

Question 177049: Verify algebraically, that (Fof^-1)(x)=x for f(x)=1/(2x+4)
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Your problem statement is a little unclear! Did you mean to write:
Verify algebraically that for
I'll assume that you did and we'll proceed.
First, we find
Start with the given function, but replace the with :
Now exchange the x and the y.
Next, solve this for y. Multiply both sides by (2y+4)
Divide both sides by x.
Subtract 4 from both sides.
Simplify the right side.
Now divide both sides by 2.
Finally, replace the with

Now you can find
but , so...
Simplifying this...

so...
and so
for
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