Question

Given that f (x) = x^2 + 3x + 6 and g (x) = x - 3 /2 solve for f (g (x)) when x = 1

Answer 1

First, set x=1 in g(x):
$$
g(1)=1-\cfrac{3}{2}=-\cfrac{1}{2}
$$
This now becomes the input to f(x), where here \(x=-\cfrac{1}{2}\):
$$
f(-\cfrac{1}{2})=?
$$
Does this make sense?