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Graphs and Functions

Proof f(x)=x

Suppose that F is a continuous function on [0,1] and f(x) is in [0,1] for each x. Prove that f(x)=x for some x.

Function : Analytically Find the Inverse

Please see the attached file for the fully formatted problems. Please, find analytically inverses of the following functions. a. f(x)= √(x-a)/(√(x-a) + √(b-x)) b. f(x)= (x-a)^2.5/((x-a)^2.5 + (b-x)^2.5) Where a and b are constants. Please, note that analytical solution does not require substitu

Vectors, graphs, and counting

Project 4A 1. Explain why vectors QR and RQ are not equivalent. 2. Explain in your own words when the elimination method for solving a system of equations is preferable to the substitution method. 1. In Washington DC, there is a large grassy area south of the White House known as the Ellipse. It is actually an ellipse wi

Shortest segment

If P is any point on the parabola y = x^2 except for the origin, let Q be the point where the normal line intersects the parabola again. Find the shortest possible length of the line segment PQ.

Continuous function

F(x)= square root of x - 2(the 2 is not a part of the square root)/ x-4 ; x=2 decide if the given function is continuous at the specified value of s.

Composite function

Obtain the composite functions f(g(x)) and g (f(x)), and find all (if any) values of x such that f(g(x)) = g (f(x)) f(x)= the square root of 2x+1, g(x)= 1-3x

Word problems, graphs and equations, etc.

1 In a class, there are 20 men and 15 women. Find the ratio of the number of men to the number of students in the class. First express the ratio as a fraction reduced to lowest terms. Then re write the ratio using a second method. 2.Determine whether each of the ordered pair is a solution of 3x-4y>7: (0,0), (3,-6), (-

Lattice Point and Distance Formula

I need help understanding the following problem set. 1. Mark a point at the intersection of two rulings. The lattice point. Seven units to the right and four units up, mark another. Use a ruler to find the distance from one point to the other, using the distance between two parallel rulings as the unit. What degree of ac

Directed Graphs and Trees

A. Is a directed graph weakly connected if there is a path from a to b and from b to a whenever a and b are vertices in the graph? b. If two trees have the same number of vertices and the same degrees, are the two trees isomorphic?

More Tree Trans

A. The length of the longest simple circuit in K5 is ???? b. If T is a tree with 999 vertices, then T has ???? edges.

Function problem

If F(x)=x/x+1 find F(x+h)-F(x)/h where h is not 0. This problem wants you to substitute F(x+h)-F(x)/h into F(x)=x/x+1.

Directed Graphs

Given the adjacency relation p = {(1,4), (1,5) (1,6), (6,2), (6,3), (6,5)} on the set N ={1,2,3,4,5,6}, find the corresponding directed graph and adjacency matrix.

Graphs and Their Representations

If all the nodes of a simple, connected, planar graph have degree 4 and the number of arcs is 12, into how many regions does it divide the plane?

Big-Oh Function

Please see the attached file for the fully formatted problems. I need to find the best big-oh function for the function. I need to choose my answer from among the following: 1, log2 n, n, n log2 n, n2, n3,..., 2n, n!. A. f(n) = 1 + 4 + 7 + ... + (3n + 1). B.

Cost Problem (Using Graph - Slope)

If 9 pounds of pears cost x dollars, then what is the price per pound? Use the equation of a straight line and call y = "x $" and x = "9 pounds" and solve for the slope "m"

Moment generating function

1. X is uniform on {1,2,3,4,5,6} m_x(s)=? m_x(s)=E(e^sX) Which is called the moment generating function of X (or the distribution of X)


Which functions are one-to-one? Which functions are onto? Describe the inverse function A)F:Z^2-N where f is f(x,y) x^2 +2y^2 B)F:N->N where f is f(x) = x/2 (x even) x+1 (x odd) C)F:N->N where f is f(x) = x+1 (x even) x-1 (x odd) D)h:N^3 -> N where h(x,y,z) = x + y -z

Question about onto functions

Let P be the power set of {A, B} and let S be the set of all binary strings of length 2. A function f: P -> S is defined as follows: For A in P, f(A) has a 1 in the high-order bit position (left end of string) if and only if a is in A. f(A) has a 1 in the low-order bit position (right end of string) if and only if b is in A. Is

Equation of the tangent line

Find the equation of the line to y = x^(sin x) at the point [(pie/2),(pie/2)] Show all work and reduce to lowest terms.