answer each part

injective functions ( = one - to- one ) Let f: A -B be a function. 1. Complete the definition : f is called injective if Vas, aze A fla, ) = fraz ) = .. 2. Consider the function f: 1R-R defined by f (x )= 1x1. ( a) Can it happen that X1, X2 ER, X1# X2 But 1X1/= 1X21? Y or N (encircle) If YES, give an example of such X, and X 2. (b ) Same question in more formal forme: true or false: V X 1, X 2 E RR, 1X , 1 = 1X 21 => X 1 = X2 If F, give a counterexample. ( c) Conclusion: of is injective of is not injective ( encircle) 3. Consider the function f: R - R defined by f (x) = 3x+ 1. ( a) Can it happen that x ,, X ZER, X, # X2 but f (x1) = f (x2)? yorN If yes, give an example of such X, and X2 . ( b) True or false : Vx1 , X Z E R, f(X1) = f(Xx)=> X1 = X2 If F, give a counterexample. ( c) Conclusion : of is injective . f is not injective (encircle) 4 . Let Rx = {XERIXSo'} and consider the function f: Ro- R defined by f(xs = * ?. ( a) True or false : V x 1, X 2 E Rxo , X1 # X 2 => f (x+) # f(x2) If F, give a counterexample. ( b) Conclusion : of is injective of is not injective ( encircle)