Math Answers

Create a logarithmic function in the form f(x) = log_a(x + b) and find its inverse. Show all of your solution steps to earn full credit. Your answer must include:

• A logarithmic function with a base value for a and a constant value for b
• Steps showing how you found your function's inverse
• The inverse function stated in function notation, f ^-1(x)

Provide 2 graphs, one that is a one-to-one function and one that is not a one-to-one function. Justify each classification.

Which two of the three functions are inverses of one another? Explain how you verified that two functions are inverses of one another using composition of functions and show your math work.

f (x) = ³√ x- 4 ( imagine if the tip of the symbol went to the end at 4 )

g(x) = x³ − 4

h(x) = x³ + 4

The regular price of a computer is x dollars. The price of a computer after a discount is given by f(x) = x − 400. The price of a computer after a 25% discount is given by g(x) = 0.75x . Use composition to show the new function that represents a $400 discount being taken then a 25% discount being taken.

Solve the equation -x² + 1 = x − 1 graphically. Your answer must include:

• A hand-drawn or calculator-created image of the graph with the equations f(x) and g(x) identified, along with labeled axes and any point(s) of intersection
• A statement listing the solution(s) to the equation
• Your work verifying that the solution(s) create a true statement in the original equation

The city council wants to sponsor 150 bags for their organization’s scholars. Each bag

costs $375. If they were to buy from the factory, they will be given 45% off the total

purchase. However, if they buy from the store they will be given 50% off the price for

each bag. Where will they have a cheaper purchase?

Dan works in an insurance company. Last January, he was able to insure 2 persons. Last February, he was able to insure 3 persons. Last March, he was able to insure 5 persons. Assume that the samples of size 2 are randomly selected with replacement. Find the following:

a. The population mean

b. The population variance

c. The population standard deviation

d. The mean of the sampling distribution of means

e. The standard deviation of the sampling distribution of the sample means

Show that the square of an even number is an even number using direct proof

About 23 out of 100 BSBA major in OM students can perfect their Math exam. Assuming that the probability applies the same with the other majors, what is the probability with the remaining 3300 BSBA students?

Buildmazing Developers need an amount of money to expand their business. They secure a loan at an

interest rate of 10,5% per year, compounded annually. The outstanding balance will be repaid in equal

payments of R137 828,00 at the end of each year for the next seven years. Considering the amortisation

schedule, the principle repaid during the first three years, rounded to the nearest rand,is