Question
In: Advanced Math
Consider functions f : {1,2,3,4}→{1,2,3,4,5,6}. a) Give an example of one such function (use 2-line notation)....
Consider functions f : {1,2,3,4}→{1,2,3,4,5,6}.
a) Give an example of one such function (use 2-line notation). Then say how many such functions there are and why your answer makes sense.(25 points)
(b)Give one example of such a function that is injective and one that is not. Then say how many injective functions there are and why your answer makes sense.(50 points)
(c) Explain why there are no surjective functions with this domain and codomain. (25 points)
Solutions
Colby Messinger answered 2 years agoRelated Solutions
2. Let A = {1,2,3,4}. Let F be the set of all functions from A to...
2. Let A = {1,2,3,4}. Let F be the set of all functions from A
to A. Recall that IA ∈ F is the identity function on A given by
IA(x) = x for all x ∈ A. Consider the function E : F → A given by
E(f) = f(1) for all f ∈ F.
(a) Is the function E one-to-one? Prove your answer.
(b) Is the function E onto? Prove your answer.
(c) How many functions f ∈...
Differentiate the following functions, taking care to use the correct notation for the derivative function: Can...
Differentiate the following functions, taking care to use the
correct notation for the derivative function:
Can I get the step by step solution for this please thanks
1) f(x)=(x2+2x)(3x-9)
2) y=9x2-3x/x-1
3) y = 3(8x2 + 4x)3
4) y=3xex^2
Give an example of a function F which is the joint probability distribution (not density) function...
Give an example of a function F which is the joint probability
distribution (not density) function of a pair of random variables X
and Y such that
(a) X and Y are independent and discrete
(b) X and Y are dependent and discrete
(c) X and Y are independent and continuous
(d) X and Y are dependent and continuous
Consider the function f(x)=arctan [(x+6)/(x+5)] Express the domain of the function in interval notation: Find the...
Consider the function f(x)=arctan [(x+6)/(x+5)] Express the
domain of the function in interval notation: Find the y-intercept:
y= . Find all the x-intercepts (enter your answer as a
comma-separated list): x= . Does f have any symmetries? f is even;
f is odd; f is periodic; None of the above. Find all the asymptotes
of f (enter your answers as comma-separated list; if the list is
empty, enter DNE): Vertical asymptotes: ; Horizontal asymptotes: ;
Slant asymptotes: . Determine the...
Consider the function f(x)=arctan [(x+6)/(x+5)] Express the domain of the function in interval notation: Find the...
Consider the function f(x)=arctan [(x+6)/(x+5)]
Express the domain of the function in interval notation: Find
the y-intercept: y= . Find all the x-intercepts (enter your answer
as a comma-separated list): x= . Does f have any symmetries? f is
even; f is odd; f is periodic; None of the above. Find all the
asymptotes of f (enter your answers as comma-separated list; if the
list is empty, enter DNE): Vertical asymptotes: ; Horizontal
asymptotes: ; Slant asymptotes: . Determine the...
Consider the function f(x) = x^3 / x − 2 1. Give the intervals of increase...
Consider the function f(x) = x^3 / x − 2
1. Give the intervals of increase and the intervals of decrease
for f(x).
2. Give the location of any local maximums and local minimums on
the graph of y = f(x). Give your answer(s) as a point, listing both
the x-coordinates and y-coordinates.
3. List the intervals of concavity for f(x).
4. Identify any inflection points on the graph of y = f(x). Give
your answer(s) as a point, listing...
1. Use the derivative function, f'(x)f′(x), to determine where the function f(x)=−2x^2+14x−8 is increasing. 2.Use the...
1. Use the derivative function, f'(x)f′(x), to determine where
the function
f(x)=−2x^2+14x−8
is increasing.
2.Use the derivative function f'(x)f′(x) to determine where the
function f(x)=2x^3−27x^2+108x+13 is increasing.
3.Use the derivative function f'(x)f′(x) to determine where the
function f(x)=2x^3−27x^2+108x−12 is decreasing.
4.Find each value of the function f(x)=−x^3+12x+9 where the line
tangent to the graph is horizontal.
x=
2. Use Σ-notation to write down an example of a series for which the ratio test...
2.
Use Σ-notation to write down an example of a series for which the
ratio test is inconclusive but the integral test is conclusive. You
don’t need to show how you got your answer, but you should show
that your answer is correct.
Consider the function and the value of a. f(x) = −2 x − 1 , a...
Consider the function and the value of a.
f(x) =
−2
x − 1
, a = 9. (a) Use mtan = lim h→0
f(a + h) − f(a)
h
to find the slope of the tangent line mtan =
f '(a).
mtan =
(b)Find the equation of the tangent line to f at x =
a.
(Let x be the independent variable and y be
the dependent variable.)
Please Consider the function f : R -> R given by f(x, y) = (2 -...
Please Consider the function f : R -> R given by f(x, y) = (2
- y, 2 - x).
(a) Prove that f is an isometry.
(b) Draw the triangle with vertices A = (1, 2), B = (3, 1), C =
(3, 2), and the triangle with vertices f(A), f(B), f(C).
(c) Is f a rotation, a translation, or a glide reflection?
Explain your answer.
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