Given a function I and a subset A of its domain, let I(A) represent the range of lover the set A; that is, I(A) = {I(x) : x E A}
. 12 Chapter 1. The Real Numbers (a) Let f(x) = x2. If A = [0,2] (the closed interval {x E R : ° ~ x ~ 2}) and B = [1,4]' find f(A) and f(B). Does f(A n B) = f(A) n f(B) in this case? Does f(A U B) = f(A) U f(B)? (b) Find two sets A and B for which f(A n B) =1= f(A) n f(B). (c) Show that, for an arbitrary function g : R ---+ R, it is always true that g(A n B) ~ g(A) n g(B) for all sets A, B ~ R. (d) Form and prove a conjecture about the relationship between g(A U B) and g(A) U g(B) for an arbitrary function g.
Since both of the angles are supplementary, you'd set the expressions up into an equation equal to 180(degrees). So, your equation should look like: 22x + 4 + 35x + 5 = 180. Next, you combine your like terms so that your next move will look like: 57x + 9 = 180. Then you'd follow the subtraction and division property, so your next moves will look as the following: 57x + 9 - 9 = 180 - 9 equals 171 57x / 57 = 171 / 57 equals 3 So, finally, your answer is: x = 3.