Posted by Stacy on Wednesday, June 24, 2009 at 11:24pm.
The definition of a composite function:
f º g (x) means f (g(x) ), which tells you to work out g(x) first, and then fill that answer into f. See
http://www.worsleyschool.net/science/files/composite/functions.html
In this case,
f(x) = 6/x-1 and g(x) = 1+3/x
so
f º g (x)
=f(g(x))
=f(1+3/x)
=6/(1+3/x)-1
=6x/(x+3)-1
=(6x-(x+3))/(x+3)
=(5x-3)/(x+3)
and the composite function would be?
A.(fog)(x)= (2x)
B.(fog)(x) =2/x
C.(fog)(x)=(6/x-1)(1+3/x
D.(fog)(x)=1+18/x(x-1)
There is probably a mis-interpretation of the parentheses:
f(x) = 6/(x-1) and g(x) = 1+3/x
so
f º g (x)
=f(g(x))
=f(+3/x)
=6/(1+3/x-1)
=6/(3/x)
=2x
If this is the case, the answer is (A).
This is what I thought as well. Thanks!
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