if f(x)=1/(x-2) and g(x)=4/x, what is (f*g)(x)?
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The functions given are f(x) = 1/(x - 2) and g(x) = 4/x.
(f*g)(x) = fog(x) = f(g(x)).
To find f(g(x)), first we find g(x). g(x) = 4/x.
Substituting this in f(x)
=> f((4/x))
=> 1/ ((4/x) - 2)
=> 1 / [(4 - 2x)/x]
=> x / (4 - 2x)
Therefore the required result is x / (4 - 2x)
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f(x) = 1/(x-2)
g(x) = 4/x
We need to find the function f*g(x)
==> f*g(x) = f(g(x))
We will substitute with g(x) = 4/x
==> f(g(x)) = f(4/x).
Now we will substitute with 4/x in place of x in f(x).
==> f(g(x))= 1/(4/x - 2)
==> f(g(x)) = 1/ (4-2x)/x
==> f(g(x)) = x/(4-2x)
= x/2(2-x)
==> f*g(x) = x/ 2(2-x)