1. Each of the following formulas defines a function from R to R. Which of the functions are one-to-one? Justify your answer. (a) f(x) = 1. (b) i(x) = 31 + 2. 1 (c) i(x) = Jac| + 1 2. Each formula defines a function from R to R. Which of the functions are onto? Prove that your answers are correct. (a) j(r) = (3r - 4)/5. (b) d(r) = Vr+5 -5. 3. Each formula defines a function from R to R. Which of the functions are bijections? Prove that your answers are correct. (a) f (t) = \\+ + 1. (b) g(u) = Vu -5. 4. Let f : R+ -> R+ is defined by f(x) = vr +1 - 1 and g : R+ - R+ is defined by g(x) = 12 + 2x. Verify that g is the inverse of f. 5. Suppose f : A - B and g : B - C. (i) Show that if f and g are bijections, then go f is a bijection. (ii) Show that if f and g are bijections, then (gof) 1 = f-log-1. 6. Assume f : A - B. Show that if A, and A, are subsets of A, such that A2 C Al, then f(A2) C f(A])