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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))=
explain the differences between a balanced transportation model and an unbalanced transportation model.when do you have
for the following use the spearman rank correlation coefficient to test the claim. identify and state the null and
Create an activity (e.g., a worksheet, a computer program, etc) that uses mathematical modeling of another context. Identify the Common Core State Standards content standards that your activity addresses. Provide solutions for your activity.
Compute and interpret the meaning of the instaneous rate of change at t=11
e 0.03. A sample of 9 players is selected at random. What is the probability that the sample contains no defective units? (Round your answer to four decimal places.)
Buying a Cottage A group of friends decides to buy a vacation home for $120,000, sharing the cost equally. If they can nd one more person to join them, each persons contribution will drop by $6000. How many people are in the group?
Assume that the average loan on a home is quoted to be $55,000.00. Calculate the monthly repayment necessary to have the loan repaid after 25 years if the interest rate is 7.5%.
The ages of workers in the Illuminex plant are approximately normally distributed with a mean of 42 years and a standard deviation of 10 years. A worker is stopped at random and asked to fill out a questionnaire. What is the probability that this ..
Find the y-coordinate of the point (3+h, ) if this point lies on the graph of the function F(x) = (3/x) - x the y-coordinate of the point is.
a math student has a 100 homework average and test grades of 99,100 and 97. what is the lowest grade the student can get on the final exam and still get an A (an average of 90 or better) in the class?
Three workers sort 66 boxes in a day. One of the workers is three times more productive than the second worker and twice as productive as the third worker. How many boxes did the second most productive worker sort?
A vat with length 6 meters, width 4 meters, and depth 3 meters is filled with water to a depth of 2 meters. Find the work required to pump all the water to the top of the vat. The weight density of water is 9810 N/m^3
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