We are told that h(x) = 1 / (x+2) and k(x) = 3x - 4. We want to find h(k(x)), or (h o k)(x). We work INSIDE OUT.
h(k(x)) = h(3x - 4).
Now we take the function, 3x - 4, and apply what h(x) wants us to do.
Evaluating h(3x - 4) means that we put the 3x - 4 into h(x).
h(x) = 1 / (x+2)
So h(3x -4) = 1 / (3x -4) + 2 <---- notice how x was the same. so are the 3x -4 parts
= 1 / 3x - 2
Thus, the composition is [tex] \frac{1}{3x-2} [/tex]
