Consider the following functions from ℤ × ℤ → ℤ. Which
functions are onto? Justify your...
Consider the following functions from ℤ × ℤ → ℤ. Which
functions are onto? Justify your answer by proving the function is
onto or providing a counterexample and explaining why it is a
counterexample.
(a) f(x,y) = xy + 3
(b) f(x,y) = |xy| + 10
(c) f(x,y) = ⌊(x+y)/5⌋
Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let...
Let Let A = {a, e, g} and B = {c, d, e, f, g}. Let f : A → B and
g : B → A be defined as follows: f = {(a, c), (e, e), (g, d)} g =
{(c, a), (d, e), (e, e), (f, a), (g, g)}
(a) Consider the composed function g ◦ f.
(i) What is the domain of g ◦ f? What is its codomain?
(ii) Find the function g ◦ f. (Find...
Consider ℝ with the standard topology and the map f : ℝ
→ {–1, 0, 1}...
Consider ℝ with the standard topology and the map f : ℝ
→ {–1, 0, 1} defined by:
f(x) = {–1 when x > 10; 0 when –10 ≤
x ≤ 10; and 1 when x < –10}.
Select each and every set that is an open sets in the quotient
topology on {–1, 0, 1} (there are 3 out of 5).
A. {–1,0,1}
B. {0}
C. {0,1}
D. {–1}
E. {–1,1}
This is all that I have. This question...
Which of the following are one-to-one, onto, or both?
a. f : Q → Q defined...
Which of the following are one-to-one, onto, or both?
a. f : Q → Q defined by f(x) = x3 + x.
b. f : S → S defined by f(x) = 5x + 3.
c. f : S → S defined by:
?(?) = {
? + 1 ?? ? ≥ 0
? − 1 ?? ? < 0 ??? ? ≠ −10
? ?? ? = −10
d. f : N → N × N defined by f(n)...
Let A, B, C be sets and let f : A → B and g :...
Let A, B, C be sets and let f : A → B and g : f (A) → C be
one-to-one functions. Prove that their composition g ◦ f , defined
by g ◦ f (x) = g(f (x)), is also one-to-one.
Let f be the function defined by f(x)=cx−5x^2/2x^2+ax+b, where
a, b, and c are constants. The...
Let f be the function defined by f(x)=cx−5x^2/2x^2+ax+b, where
a, b, and c are constants. The graph of f has a vertical asymptote
at x=1, and f has a removable discontinuity at x=−2.
(a) Show that a=2 and b=−4.
(b) Find the value of c. Justify your answer.
(c) To make f continuous at x=−2, f(−2) should be defined as
what value? Justify your answer.
(d) Write an equation for the horizontal asymptote to the graph
of f. Show the...