Problem 4. Consider the following functions. For each function: 1. draw the function diagram 2. determine if it is one-to-one, onto, and invertible. If a function is invertible, provide the inverse function. Justify each of your answers. 4(a) Let Az = {1,2,3}. Let f2: P(A2) → {0,1,2,3} be the function defined by f2(X) = |X|. Note that XSA2 4(b) Let f3: {ab}3 → {ab}3 defined by f3(S1s2s3) = S3S182. Note that the input is of the form s = S1s253, the 3 characters forming the string s.

4. Find the inverse of the one-to-one function. A f-¹(x) = √√√x - 6 ******* B. f-¹(x) = √√x + 216 -1 C. f-1 (x) = √√x + 6 f(x) = (x-6)³ D. f-¹ (x) = √√x + 6 -1 5 Find the distance between the pair of points. 10 (-4,-3) and (-8,0)

4. 7. Function fis given below. Find the inverse of the function. f(x)=√x+4-4 A. (x)=√x-4+4 B. ¹(x)=(√x+4-4) C. f(x)=(x-4)³ +4 D. (x) = (x+4)³ - 4 1 *Show/Illustrate/Explain all work that leads to your answer*

7. Find the inverse of the following function. Restrict the domains of f and f-1 if necessary: f(x) = Vx + 3