Let f(x) = 6/x-1 and g(x) = 1+3/x. Please find the composite function of (fog)(x)
(fog)(x) is a notation for substituting g(x) for x in the definition of f(x), in other words,
(fog)(x) = f(g(x))
Using f(x) = 6/x-1
and g(x) = 1+3/x
you would find
(fog)(x)
= f(g(x))
= 6/g(x) -1
= 6/(1+3/x) - 1
= (5x-3)/(x+3)
So in other words the final answer would be what? I got 2x. Is this correct?
I got (5x-3)/(x+3).
Can you show me how you got 2x?
Actually, it slipped my memory:
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).
See:
http://www.jiskha.com/display.cgi?id=1245900271
To find the composite function (fog)(x), we need to substitute the function g(x) into f(x).
Step 1: Replace x in f(x) with g(x) to form f(g(x)):
f(g(x)) = f(1+3/x)
Step 2: Substitute the expression for g(x) into f(x):
f(1+3/x) = 6/(1+3/x) - 1
Step 3: Simplify the expression:
To simplify the expression, we need to have a common denominator:
6/(1+3/x) - 1 = 6/(1+x/3) - 1
To have a common denominator, we multiply the numerator and denominator of the first fraction by 3:
6/(1+x/3) - 1 = (6*3)/(3*(1+x/3)) - 1
= 18/(3 + x) - 1
Therefore, the composite function (fog)(x) is given by:
(fog)(x) = 18/(3 + x) - 1