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if f(x)=1/(x-2) and g(x)=4/x, what is (f*g)(x)?

| Certified Educator

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)

Approved by eNotes Editorial

| Certified Educator

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)

Approved by eNotes Editorial

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