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1) The one-to-one functions g and h are defined as follows. g={(-1, 0),( -0, 3), (-1, 7), (-3, 5)} =h(x)=-3x10 Find the following. g^-1(0) = h^-1(x) = (h°h^-1)(8) = 2) Suppose that the relation S is defined as follows. =S{(5, 8),( -0, 3), (-3, 3),( -5, 3)} Give the domain and range of S . Write your answers using set notation. 3) Suppose that the functions r and s are defined for all real numbers x as follows. r(x)=x-1 s(x)=2x^2 Write the expressions for (r+s)(x)= and (r*s)(x)= and evaluate (r-s)(2)= 4) Suppose that the functions p and q are defined as follows. p(x)=x^2+7 q(x)= √x+8 Find the following. (p°q)(1)= (q°p)(1)= 5) Suppose that the function f is defined , for all real numbers, as follows. f(x)={-1/2x-2 if x≠1 {-4 if x=1 Find the following. f(-2)= f(1)= f(4)= 6) For each pair of functions f and g below, find f(g(x)) and g(f(x) . Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) f(x)=2x g(x)=x/2 f(g(x))= g(f(x))= (b) f(x)=2x+3 g(x)=x+3 /2 f(g(x))= g(f(x))=
One of the most famous unsolved problems in mathematics is a conjecture made by Christian Goldbach in a letter to Leonhard Euler in 1742. The conjecture made in this letter is now known as Goldbach's Conjecture. The conjecture is as follows:
You withdraw $10 from a bank account once a week for four weeks. What integer Expresses the change in value?
If the wages per hour are $10, $15, and $18 for low, medium, and high skilled, respectively, how many of each type should be hired to minimize total hourly wages?
in a company with 3000 employees, the monthly salaries are normally distributed. The mean salary is $2700, with a standard deviation of $400. About how many of the employees earn more than $2460 per month?
What is the probability that the sample mean breaking strength for a random sample of 40 rivets is between 9950 and 10,250? If the sample size had been 15 rather than 40, could the probability requested in part (a) be calculated from the given inf..
a genetic condition is found that affects 10 of adults in the us population. in a city with 100000 that means that
A jeweler has three small solid spheres made of silver, of radius 5 mm, 2 mm, and 6 mm. He decides to melt these down and make just one sphere out of them. What will the radius of this larger sphere be?
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application of algebra to find the weekly revenueif a manufacturer charges q dollars each for footballsnbspthen he can
Train A leaves a station traveling at 64 kilometers per hour. Two hours later, train B leaves the same station traveling in the same direction at 84 kilometers per hour. How long does it take train B to catch up to train A?
Probability distribution of the model, Alice Tanner is a nurse on the night shift from 10:00 P.M. to 6:00 A.M. at Community Hospital. She has 15 patients for whom she is responsible in her area
christmas is coming and your son lets it be known that he wants a football made from a certain brand name that he does
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