MATH 120 Midterm: MATH 120 UW 120solnsA01
Document Summary
Autumn 2001: recall that f (x) = 2x + 3 for this problem. (a) to nd f (g(x)), we compute: f (g(x)) = f(cid:18) 1. To simplify this, we multiply the top and bottom of the (larger) fraction by 2x + 3: f (g(x)) = 2x + 4 (b) the domain of f (g(x)) is the set of x which are in the domain of g and for which g(x) is in the domain of f . The domain of f is {x : x 6= 1}, and the domain of g is {x : x 6= 3/2}. Thus x is in the domain of f (g(x)) if x 6= 3/2 and g(x) 6= 1. 5 x is two rays, or half-lines : Autumn 2001: in the picture (to the right), we have added the labels x and d and x + 18. We are trying to nd the quantity d.
