MTH 001 β HW5Chapter 5

Spring 2020

Name:

Question 1: Let π(π₯) =

ID: __________________________

2π₯β5

π₯+1

, find π β1 (π₯) and its domain and range.

3

Question 2: Let π(π₯) = βπ₯ β 2 + 3.

a) Is π(π₯) one to one, why?

b) If π(π₯) is one to one, find π β1 (π₯).

Question 3: Find the domain of the following functions.

(π₯+2)(π₯β3)

a) π(π₯) = log (

)

(π₯β8)

b) π(π₯) = ln(π₯ 2 β 4)

1

Question 4: Let π(π₯) = 5π₯

a) Sketch the graph of π(π₯).

b) Is π(π₯) one to one, why?

c) If π(π₯) is one to one, find π β1 (π₯).

d) Deduce the graph of π β1 (π₯).

Question 5: Let π(π₯) = πππ2 π₯

a) Sketch the graph of π(π₯).

b) Is π(π₯) one to one, why?

c) If π(π₯) is one to one, find π β1 (π₯).

d) Deduce the graph of π β1 (π₯).

Question 6:

a) Write the following as a single logarithm:

1

2

b)

(log(π₯ + 7) β 3 log(π₯ β 5) β log(π₯ 2 + 4) + 2 log(π₯ + 6))

Write the following as sum and difference of Logarithms:

πππ

3

β

(π₯β2)2 (π₯+4)

π₯ 5 (π₯β7)3

2

Question 7: Solve the following equations:

a) 32π₯β3 = 53π₯+1

2

b) 9βπ₯ . 3β5π₯ =

1

27

c) π 2π₯β3 = 7

d) log(2π₯ + 1) β log(π₯ β 2) = 1

e) log π₯ + log(π₯ + 4) = log 12

f) πππ6 (π₯ + 2) + πππ6 (π₯ + 3) = 1

3

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