answer each part

GL MATH 1650: ASSIGNMENT #3 5. Consider the function f: [- 2, 2] - R defined by f (x)= x21. ( a ) True or false : VX 1, X 2 E [- 2, 2], f (x1)= f(X2)=> X1 = X2 If F , give a counterexample . ( b) Conclusion: of is injective of is not injective 6. For a function f: A - B, which of the following are equivalent to the condition "f is injective "? Encircle. ( a) Every 6 EB has at least one preimage in A . Recall that f (8 ) ( 6) There exists BEB such that f(6) = $. denotes the full preimage of the ( c ) Every BEB has at most one preimage in A. element 6 . (d ) V 6EB , f"' ( 6 ) + 0. ( e) For every BEB, the set f"(6) has at most one element. ( f ) For as, az EA, if a, # a2, then necessarily fla,) + f(a2). ( 9) For as, a2EA, if an = a2, then flai)= f(az). ( h ) = a1 , a 2 E A such that an tas but fla, ) = flaz). (is Van, a 2EA, flan ) = f(a2) => an= a2 ( j) For as, a 2 EA and BEB, if flar ) = band fla2)= 6, then a, = a2. ( K ) Forevery BEB, the equation f (x ) = 6 has at most one solution XE A . ( 2 ) For every BEB, the equation f (x) = 6 has at least one solution XEA