(11) Consider the Gelfand-Shilov function given by: if x 0, Φλ (2) = if r≤0. with Re(A) > 0. Show that a(z) × 03(x) = 0α+3(x). *

If f = {(0, 1),(1, 2)}, (b) find h(x) = f(5 − 3x) − 2.

Suppose that f(z) = x² - y² - 2y + i(2x - 2xy), where z = x+iy. Write f(z) in terms of z, and simplify the result. (Hint: You may prove and use the expressions x = and y =

1. Given the functions, f(x) a. Find Ag(4)). * and , g(x) = Vĩ. b. Find fAg(x)). c. Find g(f(4)). d. Find g(fx)). 2. Consider the functions, h(x) = 3x - 7 and k(x) = . a. Find h(k(-2)) b. Find h(k(x)) c. Find k(h(-2)) d. Find k(h(x)) 3. Consider the functions, m(x) = x + 3x and p(x) = 2x + 5, Find m(p(1)) b. Find m(p(x)) a. c. Find p(m(1)) d. Find p(m(x)) 4. Consider the functions b(x) = (x – 1) and c(x) = Vx+1, b. Find b(c(x)) a. Find b(c(9)) d. Find c(b(x)) c. Find c(b(9))

Let t(x) = 2x - l and m(x) = x – X. Find m(t(x)) Be sure to simplify your answer. Use the fx button to type in the answer as needed.

Suppose that the functions q and r are defined as follows. q (x) =x² +9 r (x) = /x+8 Find the following. (r o 4) (8) = O (g o r)(8) = 0