Question 3. let f: x --> y be a function. (a) recall that for c cy, the inverse image of c is the set f-1(c) = {x e x|f(x) e c}. let a, b cy. prove that f-1(anb) cf-1(a) n f-1(b). (b) recall that for d c x, the image of d under f is the set f(d) = {f(x) e yx e x}. let a, b c x. prove that f(an b) c f(a)n f(b). find an example of a function f and sets a and b such that f(anb) = ø but f(a) n f(b) + ø.

A. plot the data for the functions f(x) and g(x) on a grid and connect the points. x -2 -1 0 1 2 f(x) 1/9 1/3 1 3 9 x -2 -1 0 1 2 g(x) -4 -2 0 2 4 b. which function could be described as exponential and which as linear? explain. c. if the functions continue with the same pattern, will the function values ever be equal? if so, give estimates for the value of x that will make the function values equals. if not, explain why the function values will never be equal.