Recall: What are the two restrictions on the domain of a function? (We will learn a new restriction in Chapter 4 when we discuss logarithmic functions.)   When we write (f+g)(x) = f(x) + g(x) , what does this mean? Explain in your own words.     Complete the following: (f-g)(x) (fg)(x) (f/g)(x)   Explain how to find the domain of functions that are combined algebraically with addition, subtraction, multiplication, or division.     What is the formula for the difference quotient?     Define the composition of functions.     Explain how to find the domain of a composition of functions.

Q: Use the properties of logarithms to condense each expression to a single logarithm

A: Consider the given expression.

Q: How does the graph of f(x)=3log, (x+2) compare to the graph of g(x) = log,x? Paragraph BI I U✓ U✓ A…

A: Given query is to find the transformation applied.

Q: Use the function to answer the questions. S(x) = log, (x + 7)- 5 What is the domain of the function?…

A: Use property of logarithmic function

Q: Write a rule for logarithms of exponents: log, (X°) = log,(, %3D

A: Given : logbXc =       ×logb

Q: Write the expression as a single logarithm with coefficient 1. log(x – 5) + 3 log(2x + 1) – 2 log(x)

A: properties of logarithms are alogcb=logcba logca+logcb=logcab logca-logcb=logcab

Q: a. f(z) = – log:(z) = - 3 b. f(z) = log3(x) c. f(x) = - log;() d. f(x) = log:() %3D 3

A: Given: a. f(x)=-log13x b. f(x)=log3x c. f(x)= -log5x d. f(x)=log13x

Q: ? 1. log (AB) = log (A) + log (B) ? 2. In (A) In (B) = In (A) + ln (B) 3. log (vA) = log (A) log (A)…

A: 1. True Log(AB) = Log A + Log B

Q: 6. Rewrite the following expressions as a single logarithm. Show all your steps! a. log, 3+ log,…

A:

Q: Find the domain of the following functions. (Show all algebra) f(x) = log3(5 – x)

A: