1. Find (*+h)-f(2) for f(x) = V4x + 2. Simplify your answer until there are no...

 

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1. Find (*+h)-f(2) for f(x) = V4x + 2. Simplify your answer until there are no radicals in the numerator. 2. Find a formula for the function / whose graph is shown in the diagram below. 2 3 4. 6 10 3. Give the domain in interval notation for each function: 2x-5 a. f(x) = b. g(t) = v5-t+ V6 +t 4. For f(x) = v2x + 3 and g(x) = x² +1, find fog, gof, fof, and gog and give their domain in interval notation. [10 marks] 5. An electricity company charges its customers a base rate of $15 a month plus 8 cents per kilowatt-hour (kWh) for the first 1200 kWh and 12 cents per kWh for usage over 1200 kWh. Write the cost, C, in dollars as a function of x, the number of kWh used for Osx< 1500 and graph the function [S marks] 6. A certain paper book sells for $25. The author receives a royalty of 12% on the first 5000 copies sold, 15% on the next 10000 copies sold, and 20% for any additional copies sold. Write R, the amount of royalties in dollars as a function of x, the number of copies sold. -4x [12 marks] 7. For the function f(x)= Sx+2 (4 marks) a. Show that it is one-to-one. b. Find the inverse, f-). c. Check that f(f-"(x)) = x. (4 marks) (4 marks) 8. Suppose that the population of a certain species is given by P(t) = 1000 where tis given in years. [10 1marks] 1+9e-t (4 marks) a. Find the inverse of P. (4 marks) b. Use the inverse in a to find the time required for the population to reach S00. (2 marks) c. What happens to the population as time goes on, i.e. as t- co? [10 marks] 9. For the function f(x) = 2+3 Inx %3D 4-Inx (5 marks) a. Find f-(x). (5 marks) b. Check that f-(x)) = x. [10 marks] 10. Find the exact value of each expression. (3 marks) a. sin- (sin *(sin) (3 marks) b. cos-1 (4 marks) C. sin(2sin- ) 1. Find (*+h)-f(2) for f(x) = V4x + 2. Simplify your answer until there are no radicals in the numerator. 2. Find a formula for the function / whose graph is shown in the diagram below. 2 3 4. 6 10 3. Give the domain in interval notation for each function: 2x-5 a. f(x) = b. g(t) = v5-t+ V6 +t 4. For f(x) = v2x + 3 and g(x) = x² +1, find fog, gof, fof, and gog and give their domain in interval notation. [10 marks] 5. An electricity company charges its customers a base rate of $15 a month plus 8 cents per kilowatt-hour (kWh) for the first 1200 kWh and 12 cents per kWh for usage over 1200 kWh. Write the cost, C, in dollars as a function of x, the number of kWh used for Osx< 1500 and graph the function [S marks] 6. A certain paper book sells for $25. The author receives a royalty of 12% on the first 5000 copies sold, 15% on the next 10000 copies sold, and 20% for any additional copies sold. Write R, the amount of royalties in dollars as a function of x, the number of copies sold. -4x [12 marks] 7. For the function f(x)= Sx+2 (4 marks) a. Show that it is one-to-one. b. Find the inverse, f-). c. Check that f(f-"(x)) = x. (4 marks) (4 marks) 8. Suppose that the population of a certain species is given by P(t) = 1000 where tis given in years. [10 1marks] 1+9e-t (4 marks) a. Find the inverse of P. (4 marks) b. Use the inverse in a to find the time required for the population to reach S00. (2 marks) c. What happens to the population as time goes on, i.e. as t- co? [10 marks] 9. For the function f(x) = 2+3 Inx %3D 4-Inx (5 marks) a. Find f-(x). (5 marks) b. Check that f-(x)) = x. [10 marks] 10. Find the exact value of each expression. (3 marks) a. sin- (sin *(sin) (3 marks) b. cos-1 (4 marks) C. sin(2sin- )