### Find the composite functions for the given functions.

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A+ TUTORIAL FOR THE FOLLOWING QUESTIONS

**Operations on Functions**

Unit Summatives

Operations on Functions Unit Assignment

1.Find the composite functions for the given functions. (6 marks)

a.f(x) = 4x + 1 and g(x) = x2

b.f(x) = sin x and g(x) = x2 - x + 1

c.f(x) = 10x and g(x) = log x

2.State the domain and range for each resulting function in question 1. (6 marks)

3.If f = {(-2,-1), (-1,2), (0,6), (1,3), (2,-1), (3,-5), (4,0), (5,8)} and g = {(-2,6), (-1,5), (0,-8), (1,3), (2,9), (3,9), (4,0), (5,-2)}, then find . (2 marks each)

4.By graphing the functions, determine the region where log2(x+3) > 2x. (5 marks)

5.The temperature of the Earth's crust is a linear function of the depth below the surface. An equation expressing the relationship is T(d) = 0.01d + 20, with the temperature (T) in Celsius and the depth (d) in metres. d is also a function given by d(t) = st in which t is time measured in seconds and s is the speed in m/s.

a.If you were to go down the shaft of an elevator in a mine at a rate of 5 m/s, use the composition of functions to express the temperature as a function of the time travelled in the elevator in seconds. (2 marks)

b.Use this composite to find the temperature after the following amounts of time in the elevator. (2 marks)

i.5 seconds

ii.50 seconds

c.How long would it take to reach a temperature of 25C? (1 mark)

d.At what depth would this happen? (1 mark)

6.The sticker price of a new car is $n. Near the end of the model year, the manufacturer and the dealerships want to reduce their inventories as much as possible. One dealer is offering a $1500 factory rebate and a dealer discount of 5%.

a.Write an expression for R(n), the price of the new car after the factory rebate. (1 mark)

b.Write an expression for D(n), the price of the new car after the dealer discount. (1 mark)

c.Write expressions for R ? D(n) and D ? R(n). State in words what each of these is saying in terms of the price of a new car. (3 marks)

d.Ken is interested in purchasing a new hybrid vehicle whose sticker price is $30 179. Evaluate R ? D and D ? R for this vehicle. Discuss the results. (3 marks)

7.Many nations compare the value of their currency to the US dollar. On a day early in 2009, $1 CDN (1 Canadian dollar) was worth $0.8290 USD (US dollar). This is known as an exchange rate. On the same date $1 USD could be used to buy 0.7579 Euros or 0.6709 UK pounds (United Kingdom pounds Sterling).

a.Demonstrate and explain how the above exchange rates could be used to create composite functions to convert Canadian dollars to Euros or UK pounds. (4 marks)

b.I am planning a trip to Portugal, Spain and France with a side trip to England. Using your composite functions, determine how many Euros I could get for $1000 CDN and how many UK pounds for $500 CDN. (2 marks)

8.Explain what is meant by the term order of a function and state how the order of a function can be found. (2 marks)

9.Under what circumstances is always true? When is this statement true for f(x) = x2 + x 2 and g(x) = x + 4? (4 marks)

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