Please show all work

Answer all questions and show your work. 1. Find the inverse function of f ( ) _ 2x 3 a: F a: + 1 and verify f and its inverse are inverse functions of each other. 2. Consider f(:r) = 2:1:2 + 89: + 1. (a) Find the standard form of f (x) (b) Find the maximum or minimum of f (3:) 3. Sketch the graph of each function. (a) f(x) = -324 (b) 1%) = (I + 2)5 4. Describe the end behavior of the graph of each function. (a) x) 2 $332 100 (b) f(:r) = 23:3 + Sm + 100 (c) f(:r) = 3:4 100$2 + 1 5. Find all real zeros of x) = 2:r\" + 2332. Sketch its graph. 6. Show that f (at) = 2:3 1:2 + 1 has a real zero between -1 and 1. 7. Divide the polynomial 633 1912 + 163: 4 by m 2 and use the result to factor the polynomial completely. 8. Use synthetic division to divide 11:4 103:2 2m + 4 by I + 3. And, nd f(3)