Share
Explore BrainMass

Functions, Inverse Functions and Graphs

1. Let h(x) = (8x - 5)/(7-x).
(a) Find the inverse of the function h. Show work.
(b) What is the domain of h? What is the domain of the inverse of h?

2. Use a calculator (standard scientific calculator or the online graphing calculator) to find each of the following values. Write your answer rounded to 4 decimal places.
(a) e ^-0.3
(b) 6 ^ sqrt(10)

3. Let f (x) = 4^x. (Not necessary to show work for #3. Answers are sufficient.)
(a) Calculate f(3)
(b) What is the domain of f ?
(c) What is the y-intercept?
(d) What happens to the graph of f at the far left; that is, what happens to f (x) as x --> ? infinity?
[Choices: (I) Goes up (II) Goes toward 0 (III) Neither (I) nor (II) ]
(e) What happens to the graph of f at the far right; that is, what happens to f (x) as x --> infinity?
[Choices: (I) Goes up (II) Goes toward 0 (III) Neither (I) nor (II) ]

4. Let g(x) = (4/7)^x (Not necessary to show work for #4. Answers are sufficient.)
(a) Calculate g(?1)
(b) What is the do0main of g?
(c) What is the y-intercept?
(d) What happens to the graph of g at the far left; that is, what happens to g(x) as x ? ? infinity?
[Choices: (I) Goes up (II) Goes toward 0 (III) Neither (I) nor (II) ]
(e) What happens to the graph of g at the far right; that is, what happens to g(x) as x ? infinity?
[Choices: (I) Goes up (II) Goes toward 0 (III) Neither (I) nor (II) ]

5. The formula to determine the monthly payment amount (PMT) for a car loan, home mortgage, or other installment loan is given by

PMT = P * (i/12) / (1 - (1 + i/12)^-n)

where P is the amount borrowed, i is the annual interest rate (as a decimal), and n is the total number of payments.
Suppose George buys a car and obtains a 4 year loan for $20,000 at an annual interest rate of 3%.
(a) What is the monthly payment? (Show values substituted in the formula, and calculate the numerical amount, maintaining a high level of precision.)
(b) If George makes all 48 payments, how much will he have paid altogether?

Attachments

Solution Preview

Please see attached file.

1. Let
(a) Find the inverse of the function h. Show work.
Solution: Let = y.
Cross multiplying, 8x - 5 = y(7-x) = 7y - xy
Transposing, 8x + xy = 7y + 5 = x(8 + y)
Therefore, x = .
........Ans

(b) What is the domain of h? What is the domain of the inverse of h?
Solution: Domain of h = All real numbers except 7.
Domain of inverse of h = All real numbers except -8.

2. Use a calculator (standard scientific calculator or the online graphing calculator) to find each of the following values. Write your answer rounded to 4 decimal places.
(a) e -0.3 = 0.7408
(b) = 23.6243

3. Let f (x) = 4x. (Not necessary to ...

Solution Summary

Functions, inverse functions and graphs are analyzed. The expert uses a calculator to find values.

$2.19