(1) Give an inverse for each function if it exists, or else say why there is no inverse: (a) f(x) = x³, ƒ : R→ R (b) f(x) = x², ƒ: N→ N (c) f(x) = student's first name, f: {this class}→→{all names}

Find the inverse of f when its domain is restricted to the interval 0,. fx=x2+3

Differentiate the function of y = (e4x^2+1)3 in two different ways: i.) by differentiating the function without doing any algebra first   ii.) by doing as much algebraic simplification as possible beforehand

How to use the standard y = f(x) notation to indicate that (a, b) is an element of the function f?

(1a) Let A = {1, 6, 12}, B = {0, 2, 12}. The following are all relations from A to B, but which are functions? Explain why or why not? f1 = {(1, 2),(6, 0),(12, 12)} f2 = {(1, 0),(1, 2),(6, 12),(12, 0)} f3 = {(1, 12),(6, 0)} f4 = {(1, 0),(6, 0),(12, 2)}   (1b) Let X = {a, b, c, x, y, z} and Y = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Define a function f : X → Y to be: f = {(a, 2),(b, 3),(c, 7),(x, 9),(y, 4),(z, 8)}. Define a function g : Y → X to be: g = {(1, b),(2, c),(3, b),(4, a),(5, z),(6, z),(7, b),(8, x),(9, y)}. Determine the following: 1. The range of f. 2. The range of g. Do we have Rng(f) a proper subset of Codom(f)? What about for g?