MTH 001 American University of Sharjah Domain and Range Algebra Questions

MTH 001 – HW5Chapter 5
Spring 2020
Name:
Question 1: Let 𝑓(𝑥) =
ID: __________________________
2𝑥−5
𝑥+1
, find 𝑓 −1 (𝑥) and its domain and range.
3
Question 2: Let 𝑓(𝑥) = √𝑥 − 2 + 3.
a) Is 𝑓(𝑥) one to one, why?
b) If 𝑓(𝑥) is one to one, find 𝑓 −1 (𝑥).
Question 3: Find the domain of the following functions.
(𝑥+2)(𝑥−3)
a) 𝑓(𝑥) = log (
)
(𝑥−8)
b) 𝑓(𝑥) = ln(𝑥 2 − 4)
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Question 4: Let 𝑓(𝑥) = 5𝑥
a) Sketch the graph of 𝑓(𝑥).
b) Is 𝑓(𝑥) one to one, why?
c) If 𝑓(𝑥) is one to one, find 𝑓 −1 (𝑥).
d) Deduce the graph of 𝑓 −1 (𝑥).
Question 5: Let 𝑓(𝑥) = 𝑙𝑜𝑔2 𝑥
a) Sketch the graph of 𝑓(𝑥).
b) Is 𝑓(𝑥) one to one, why?
c) If 𝑓(𝑥) is one to one, find 𝑓 −1 (𝑥).
d) Deduce the graph of 𝑓 −1 (𝑥).
Question 6:
a) Write the following as a single logarithm:
1
2
b)
(log(𝑥 + 7) − 3 log(𝑥 − 5) − log(𝑥 2 + 4) + 2 log(𝑥 + 6))
Write the following as sum and difference of Logarithms:
𝑙𝑜𝑔
3
√
(𝑥−2)2 (𝑥+4)
𝑥 5 (𝑥−7)3
2
Question 7: Solve the following equations:
a) 32𝑥−3 = 53𝑥+1
2
b) 9−𝑥 . 3−5𝑥 =
1
27
c) 𝑒 2𝑥−3 = 7
d) log(2𝑥 + 1) − log(𝑥 − 2) = 1
e) log 𝑥 + log(𝑥 + 4) = log 12
f) 𝑙𝑜𝑔6 (𝑥 + 2) + 𝑙𝑜𝑔6 (𝑥 + 3) = 1
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