Question

(01.02) Given that f(x) = x2 + 3x + 6 and g(x) = the quantity of x minus three, over two , solve for f(g(x)) when x = 1. (1 point) −1 0 3 4

Answer 1

In this composite you are going to stick the g function into the f function everywhere you see an x.  So that will look like this: $f(g(x))=( \frac{x-3}{2} ) ^{2} +3( \frac{x-3}{2})+6$.  Putting in our x value of 1, now we have $f(g(1))=( \frac{1-3}{2}) ^{2} +3( \frac{1-3}{2} )+6$.  Simplifying that we have $f(g(1))=( \frac{-2}{2}) ^{2} +3( \frac{-2}{2}) +6$ which of course simplifies to 1 - 3 + 6 which is 4