Question

45 POINTS h(x) = 1/x+2 and k(x) = 3x - 4 h[k(x)] =

Answer 1

.............................

Answer 2

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 $\frac{1}{3x-2}$