For each of the following, state whether it is possible to have a function meeting the criteria given, explain why orwhy not, and if it is possible, give two examples.(a) A function f : N≥0 → N≥0 which is not surjective.(b) A function f : N≥0 → Z which is injective.(c) A function f : Q → Q which is bijective.

or each of the following functions, state whether it is injective, surjective, and/or bijective, and why.(a) The function f (n) = 2n, mapping from integers to integers.(b) The function q(ϕ), with codomain N≥0, which maps any formula of predicate logic to the number of quantifiersin that formula.

Let  be a function defined as . Then  is:Question 2Answera.Injective in b.Surjective in c.Bijective in d.Neither injective nor surjective in

1. Why is f not a function from R to R ifa) f (x) = 1/x? b) f (x) =x ? c) f (x) =2 1x  ?2. Determine whether f is a function from Z to R ifa) f (n) = ±n b) 2 1f n n  c) 214f n n 3. Find these valuesa)1.1   b)0.1   c)4   d)3.2  e)5.2   e)2   e)1 22 3      4. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one (onto)a) f (a) = b, f (b) = a, f (c) = c, f (d) = db) f (a) = b, f (b) = b, f (c) = d, f (d) = cc) f (a) = d, f (b) = b, f (c) = c, f (d) = d5. Determine whether each of these functions from Z to Z is one-to-one (onto)a) f (n) = n − 1 b) f (n) = n2 + 1 c) f (n) = n3 d) 2nf n     6. Determine whether f : Z × Z → Z is onto ifa) f (m, n) = 2m − n b) f (m, n) = m2 − n2 c) f (m, n) = m + n + 1d) f (m, n) = |m| − |n| e) f (m, n) = m2 − 4 f) f (m, n) = m + n7. Determine whether each of these functions is a bijection from R to R.a) f (x) = −3x + 4 b) f (x) = −3x2 + 7 c) f (x) = (x + 1)/(x + 2) d) f (x) = x5 + 18. Let S = {−1, 0, 2, 4, 7}. Find f (S) ifa) f (x) = 1 b) f (x) = 2x + 1 c) 5xf x     

Consider the function f: R→R defined by f(x)=sin(x)+cos(2x). Which of the following statements about f(x) is true? a. The function f(x) is one-to-one (injective). b. The function f(x) is onto (surjective). c. The function f(x) is both one-to-one and onto. d. The function f(x) is neither one-to-one nor onto.

If f is a function on a set A= {1,2,3,4,5} such that f=(1,2),(2,3),(3,4),(4,x),(5,5). Then*f is a surjective but not bijective function.f is a bijective function.f is a surjective function.f is an injective function.