4. Classify each function as injective, surjective, bijective, or none of these. Mark and justify your answers. a. f: Z*Q* defined by f (n) = n-3 f is injective / not injective because f is surjective / not surjective because f is bijective / not bijective b. f: R* R* defined by f (x) = x-³ f is injective / not injective because f is surjective / not surjective because f is bijective / not bijective

Q: Prove or disprove: composition of functions is commutative; that is g◦f = f ◦ g when both sides are…

A:

Q: d) Is the composition of two one-one functions a one-to-one function? e) Is it true that P(A) ≤ A?

A: For part (d), the answer is YES.

Q: Sketch the graph of a function f that is defined over all real numbers and that is decreasing on the…

A: Given: f(x) is decreasing on the interval -2,3. f(x) is concave down on the interval -2,2 f(x) is…

Q: Let f, g be two functions from a set A to itself. If f o g is surjective, does it imply that g o f…

A:

Q: Write out all functions f: {1,2} {a, b, c, d) (in two-line notation). How many functions are there?…

A:

Q: True or false: There exists a monotonic function f: R → R whose range is the set of integers. True…

A:

Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove the following: f(C) -…

A:

Q: Let f: P(Z x Z) → Z be a function. Which of the following correctly gives an example of an element…

A: As given, f: P(ℤ × ℤ) →ℤ  be a function.   We have to determine the example of an element from its…

Q: Let f be a function defined as follows: A jump discontinuity f(x) = What type of discontinuity does…

A: The objective of this question is to determine the type of discontinuity the given function has at…

Q: rals on which the function is concave up or down. - + 4 s an interval in the form (*, *). Use the…

A:

Q: C = {4x + 1] x € Z+}, D = {c + d]c € C, d € C}, E = C × D Is C a subset of D or E? Explain a…

A:

Q: 4. (a) (b) Let f : X → Y and g: Y→ Z be functions. Prove the following statements. If gof is…

A:

Q: How do you show the inverse image of the union of S and T equals the union of the image of S and the…

A:

Q: Let A- (Blanche, Rose, Sophia, Dorothy), B-(Red, Blue, Yellow) and consider the function f: A B…

A:

Q: 47

A:

Q: 5. Determine whether each of these functions is a bijection from R to R. (a) f(x) = 2x – 10 %3D (b)…

A: 4(d) We have to give an example of the function f:N→N that is neither one-to-one nor onto. Example:-…

Q: :N→N defined by n - the sum of thed

A: IOn this question, the concept of Injective is applied. Injective A function that links an element…