SOLUTION: Given the function f(x) = (2x-4)/x and x belongs to the real numbers and x does not equal zero, find f^2(x) The answer given in the textbook is 4 / (2-x). I can not unde

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Question 941424: Given the function f(x) = (2x-4)/x
and x belongs to the real numbers and x does not equal zero, find
f^2(x)
The answer given in the textbook is 4 / (2-x).
I can not understand how to get this answer.
I think f^2(x) = ff(x) but I don't know how to do this function.
Any help at all would be appreciated very much. I've spent over an hour trying to work this out.
Thanks
Found 2 solutions by richard1234, stanbon:
Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website!
(f of "f of x"). So just replace x with f(x).

It might be easier to rewrite f(x) as .

Then

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Given the function f(x) = (2x-4)/x
and x belongs to the real numbers and x does not equal zero, find
f^2(x)
The answer given in the textbook is 4 / (2-x).
I can not understand how to get this answer.
I think f^2(x) = ff(x) but I don't know how to do this function.
--------------------------
fof(x) = f[(2x-4)/x]
So, replace "x" in f(x) with (2x-4)/x to get
= [2[(2x-4)/x)-4]/[(2x-4)/x]
------
= [(4x-8)/x - 8]/[(2x-4)/x]
-----
= [(4x-8-8x]/x] / [(2x-4)/x]
------
= [(-4x-8)/x] / [(2x-4)/x]
------
Invert the denominator and multiply to get::
= [-4(x+2)/x] * x/[2(x-2)]
------
Cancel "x" and "2" to get::
= -2(x+2)/(x-2)
====================
Cheers,
Stan H.
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