when is (k of g)(x) if k(x)= x/x+2 and g(x)=3x+4 then simplify answer and give the domain in interval notation
To find (k o g)(x), we need to multiply k(g(x)).
First, let's find g(x):
g(x) = 3x + 4
Now let's find k(g(x)):
k(g(x)) = g(x) / (g(x) + 2)
k(g(x)) = (3x + 4) / (3x + 4 + 2)
k(g(x)) = (3x + 4) / (3x + 6)
k(g(x)) = (3x + 4) / 3(x + 2)
k(g(x)) = 4 / 3
Therefore, (k o g)(x) = 4 / 3
The domain of the composite function is the set of all real numbers except where the denominator is zero. In this case, the denominator is never zero so the domain of (k o g)(x) is all real numbers.
Therefore, the simplified answer for (k o g)(x) is 4/3 and the domain in interval notation is (-∞, ∞).