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Chapter 5: Q 37. (page 298)

Find the domain of the function.

f(x)=lnx-3

Short Answer

Expert verified

The domain of the given function f(x)is3,鈭�.

Step by step solution

01

Step 1. Given information

A logarithmic function is given asf(x)=lnx-3.

02

Step 2. Formula Used

The domain of the logarithmic function f(x)=lnxis determined by localid="1648107099601" x>0.

03

Step 3. Finding The Domain

The function is f(x)=lnx-3

Now, for the domain,

x-3>0

On solving

x>3

The required domain of f(x), using

interval notation, is 3,鈭�.

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Most popular questions from this chapter

Vehicle Stopping Distance Taking into account reaction time, the distance d(in feet) that a car requires to come to a complete stop while traveling rmiles per hour is given by the function

localid="1646198784356" d(r)=6.97r-90.39

a. Express the speed rat which the car is traveling as a function of the distance localid="1646198792401" drequired to come to a complete stop

b. Verify that localid="1646198797631" r=r(d)is the inverse of localid="1646198802104" d=d(r)by showing that localid="1646198806352" r(d(r))=rand localid="1646198811055" d(r(d))=d

c. Predict the speed that a car was traveling if the distance required to stop was localid="1646198818232" 300feet.

d(r(d))=d

Use the graph of y=f(x)given in Problem 44to evaluate

the following:

(a)f(2)

(b) f(1)

(c) f-1(0)

(d) f-1(-1)

Use the graph of y=f(x)given in the Problem 43to evaluate the following:

(a) f(-1)

(b) f(1)

(c) f-1(1)

(d) f-1(2)

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

A(n)________ is a function of the form f(x)=Caxwhere a>0,a鈮�1,and C鈮�0are real numbers. The base ais a ____ and C is a _____.

solve each equation. Verify your results using a graphing utility.

4x2=2x
See all solutions

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