(a) Define F: Z → Z by the rule F(n) = 2 - 3n, for each integer n.(i) Is F one-to-one?Suppose n, and n, are any integers, such that F(n,) = F(n,). Substituting from the definition of F gives that 2 - 3n, =Solving this equation for n, and simplifying the result gives that n, =Therefore, F is one-to-one(ii) Show that F is not onto.Counterexample:Let m =. For this value of m, the only number n with the property that F(n) = m is not an integer. Thus, F is not onto.(b) Define G: R → R by the rule G(x) = 2 - 3x for each real number x. Is G onto?Scratch work: Let y be any real number.On a separate piece of paper, solve the equation y = 2 - 3x for x. Enter the result-an expression in y-in the box below.X =(1) Is x a real number?Sums, products, and differences of real numbers are always real numbers, and quotients of real numbers with nonzero denominators are always real numbers. Therefore, x is a real number(2) Does G(y) = x?According to the formula that defines G, when G is applied to x, x is multiplied by 3 and the result is subtracted from 2.When the expression for x that you found above is multiplied by 3, the result is. And when the result is subtracted from 2, you obtainThus, G(y) = xHence, there existsa number x such that x is a real number and G(x) = y. Therefore, G is ontoNeed Help?Read It

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(a) Define F: z-Z by the rule F(n) = 2 - 3n, for each integer n. () Is Fone-to-one? Suppose n, and n, are any integers, such that F(n,) = F(n,). Substituting from the definition of F gives that 2 - 3n, = Solving this equation for n, and simplifying the result gives that n- Therefore, Fis one-to-one (i) Show that Fis not onto. Counterexample: Let m = For this value of m, the only number n with the property that F(n) - m is not an integer. Thus, Fis not onto. (b) Define G: R-R by the rule G(x) - 2 - 3x for each real number x. Is G onto?