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g

Domain: x > 5 , range: all real numbers

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g f

Domain: x > 2 and x < 4 , range: all real numbers

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Find the degree, y -intercept, and zeros for the following polynomial functions.

f ( x ) = 2 x 2 + 9 x 5

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f ( x ) = x 3 + 2 x 2 2 x

Degree of 3, y -intercept: 0, zeros: 0, 3 1 , −1 3

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Simplify the following trigonometric expressions.

tan 2 x sec 2 x + cos 2 x

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cos ( 2 x ) = sin 2 x

cos ( 2 x ) or 1 2 ( cos ( 2 x ) + 1 )

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Solve the following trigonometric equations on the interval θ = [ −2 π , 2 π ] exactly.

sec 2 x 2 sec x + 1 = 0

0 , ± 2 π

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Solve the following logarithmic equations.

Are the following functions one-to-one over their domain of existence? Does the function have an inverse? If so, find the inverse f −1 ( x ) of the function. Justify your answer.

f ( x ) = 1 x

One-to-one; yes, the function has an inverse; inverse: f −1 ( x ) = 1 y

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For the following problems, determine the largest domain on which the function is one-to-one and find the inverse on that domain.

f ( x ) = x 2 + 3 x + 4

x 3 2 , f −1 ( x ) = 3 2 + 1 2 4 y 7

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A car is racing along a circular track with diameter of 1 mi. A trainer standing in the center of the circle marks his progress every 5 sec. After 5 sec, the trainer has to turn 55° to keep up with the car. How fast is the car traveling?

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For the following problems, consider a restaurant owner who wants to sell T-shirts advertising his brand. He recalls that there is a fixed cost and variable cost, although he does not remember the values. He does know that the T-shirt printing company charges $440 for 20 shirts and $1000 for 100 shirts.

a. Find the equation C = f ( x ) that describes the total cost as a function of number of shirts and b. determine how many shirts he must sell to break even if he sells the shirts for $10 each.

a. C ( x ) = 300 + 7 x b. 100 shirts

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a. Find the inverse function x = f −1 ( C ) and describe the meaning of this function. b. Determine how many shirts the owner can buy if he has $8000 to spend.

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For the following problems, consider the population of Ocean City, New Jersey, which is cyclical by season.

The population can be modeled by P ( t ) = 82.5 67.5 cos [ ( π / 6 ) t ] , where t is time in months ( t = 0 represents January 1) and P is population (in thousands). During a year, in what intervals is the population less than 20,000? During what intervals is the population more than 140,000?

The population is less than 20,000 from December 8 through January 23 and more than 140,000 from May 29 through August 2

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In reality, the overall population is most likely increasing or decreasing throughout each year. Let’s reformulate the model as P ( t ) = 82.5 67.5 cos [ ( π / 6 ) t ] + t , where t is time in months ( t = 0 represents January 1) and P is population (in thousands). When is the first time the population reaches 200,000?

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For the following problems, consider radioactive dating. A human skeleton is found in an archeological dig. Carbon dating is implemented to determine how old the skeleton is by using the equation y = e r t , where y is the percentage of radiocarbon still present in the material, t is the number of years passed, and r = −0.0001210 is the decay rate of radiocarbon.

If the skeleton is expected to be 2000 years old, what percentage of radiocarbon should be present?

78.51%

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Find the inverse of the carbon-dating equation. What does it mean? If there is 25% radiocarbon, how old is the skeleton?

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Questions & Answers

f(x) =3+8+4
tennesio Reply
d(x)(x)/dx =?
Abdul Reply
scope of a curve
Abraham Reply
check continuty at x=1 when f (x)={x^3 if x <1 -4-x^2 if -1 <and= x <and= 10
Raja Reply
what is the value as sinx
Sudam Reply
f (x)=x3_2x+3,a=3
Bilal Reply
given demand function & cost function. x= 6000 - 30p c= 72000 + 60x . . find the break even price & quantities.
Fiseha Reply
hi guys ....um new here ...integrate my welcome
Asif Reply
An airline sells tickets from Tokyo to Detroit for $1200. There are 500 seats available and a typical flight books 350 seats. For every $10 decrease in price, the airline observes and additional 5 seats sold. (a) What should the fare be to maximize profit? (b) How many passeners would be on board?
Ravendra Reply
I would like to know if there exists a second category of integration by substitution
CHIFUNDO Reply
nth differential cofficient of x×x/(x-1)(x-2)
Abhay Reply
integral of root of sinx cosx
Wedraj Reply
the number of gallons of water in a tank t minutes after the tank has started to drain is Q(t)=200(30-t)^2.how fast is the water running out at the end of 10 minutes?
Purity Reply
why is it that the integral of eudu =eu
Maman Reply
using L hospital rule
Abubakar Reply
Practice Key Terms 7

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Source:  OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
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