1. solve the equation x = (2x+ 3)1/2
2. consider f1(x) = ln(x + 1) + ln (x-1) and f2(x) = ln(x^2-1).
a) state domains and ranges of f1 and f2.
b) sketch the curves y = f1(x) and y = f2(x).

1.  ; 2. Domain:    Range: all real numbers

Step-by-step explanation:

Let's find the solutions.

1. Solve the equation so:

Although we have two answers, remember that from the original equation the result of is never negative. So -1 do not solve the equation.

In conlcusion, the equation is solved by x=3.

2A. Domains and ranges of f1(x) and f2(x)

Using logarithmic property we have:

because:

is defined by   then:

so the domain of f1(x) is

Now for the range:

notice that is always positive, so the range of f1(x) is all real numbers.

Be aware that although point number two of the problem mentioned two equations, f1(x)=f2(x) by logarithmic properties, so their domains and ranges are the same.

2B. Graph of f1(x) is attached. Because f1(x)=f2(x) both functions plot equal.

6 on both sides and twelve on the top and the bottom

step-by-step explanation:

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.