3x - 1 (1) Let f(ac) = ac + 2 We can consider this formula as defining a function with co-domain R. However, the expression does not make sense for all x E R, so the domain of f is not R. (a) What is the maximal subset D C R for which this expression defines a function f : D -> R? (b) Let f : D - R be the function given by f (x) = 3x - 1 x + 2 , Where D is the set in (a). Find the range (or image) of f. Prove your claim. (Do not use calculus!) (2) Let f : N -+ Q be the function defined by f(x) = 223 + 6x2 + 4x 3 (a) Factor the numerator completely. (b) Explain why given three consecutive integers a, a + 1, a + 2, one of them is divisible by 3. (c) Prove that f(x) EN for all x E N. (d) Is the image (or range) of f equal to N? Justify your claim