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Functions, Inverse Functions and Graphs

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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?

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Solution Summary

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

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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 ...

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