We have the following functions:
f (x) = x ^ 2 + 1
g (x) = 1 / x
Multiplying we have:
(f * g) (x) = (x ^ 2 + 1) * (1 / x)
Rewriting:
(f * g) (x) = ((x ^ 2 + 1) / x)
Therefore, the domain of the function is given by all the values of x that do not make zero the denominator.
We have then:
All reals except number 0
Answer:
b. all real numbers, except 0
Answer: second option.
Step-by-step explanation:
In order to solve this exercise, it is necessary to remember the following properties of logarithms:

In this case you have the following inequality:

So you need to solve for the variable "x".
The steps to do it are below:
1. You need to apply
to both sides of the inequality:

2. Now you must apply the properties shown before:

3. Then, rounding to the nearest ten-thousandth, you get:

Answer:
$425
Step-by-step explanation:
Let x represent the number of bracelets made and let y represent the number of necklace made.
Since the craftsman has 1000 beads to work with, hence:
10x + 20y ≤ 1000 (1)
Also, the craftsman has 1600 minutes, hence:
10x + 40y ≤ 1600 (2)
From ploting equations 1 and 2 on the geogebra online graphing, we can see that the solution to the problem is (40, 30).
Since the bracelet costs $5 and a necklace costs $7.50, hence the maximum revenue is:
Revenue = 5x + 7.5y = 5(40) + 7.5(30) = $425
Jen has 6 crayons
Lisa has 3 crayons
Max has = lisa +1 = 4 crayons
Jen + Lisa + Max = 6+3+4 = 13 crayons
Answer: 13 crayons