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For the following exercises, use the graph of to sketch the graph of its inverse function.
For the following exercises, use composition to determine which pairs of functions are inverses.
For the following exercises, evaluate the functions. Give the exact value.
The function converts degrees Fahrenheit to degrees Celsius.
[T] The velocity V (in centimeters per second) of blood in an artery at a distance x cm from the center of the artery can be modeled by the function for
a. b. The inverse function determines the distance from the center of the artery at which blood is flowing with velocity V . c. 0.1 cm; 0.14 cm; 0.17 cm
A function that converts dress sizes in the United States to those in Europe is given by
[T] The cost to remove a toxin from a lake is modeled by the function
where is the cost (in thousands of dollars) and is the amount of toxin in a small lake (measured in parts per billion [ppb]). This model is valid only when the amount of toxin is less than 85 ppb.
a. $31,250, $66,667, $107,143 b. c. 34 ppb
[T] A race car is accelerating at a velocity given by
where v is the velocity (in feet per second) at time t .
[T] An airplane’s Mach number M is the ratio of its speed to the speed of sound. When a plane is flying at a constant altitude, then its Mach angle is given by
Find the Mach angle (to the nearest degree) for the following Mach numbers.
a. b. c.
[T] Using find the Mach number M for the following angles.
[T] The temperature (in degrees Celsius) of a city in the northern United States can be modeled by the function
where is time in months and corresponds to January 1. Determine the month and day when the temperature is
so, the temperature occurs on June 21 and August 15
[T] The depth (in feet) of water at a dock changes with the rise and fall of tides. It is modeled by the function
where is the number of hours after midnight. Determine the first time after midnight when the depth is 11.75 ft.
[T] An object moving in simple harmonic motion is modeled by the function
where is measured in inches and is measured in seconds. Determine the first time when the distance moved is 4.5 ft.
[T] A local art gallery has a portrait 3 ft in height that is hung 2.5 ft above the eye level of an average person. The viewing angle can be modeled by the function
where is the distance (in feet) from the portrait. Find the viewing angle when a person is 4 ft from the portrait.
[T] Use a calculator to evaluate and Explain the results of each.
the expression does not equal 2.1 since —in other words, it is not in the restricted domain of since 2.1 is in the restricted domain of
[T] Use a calculator to evaluate and Explain the results of each.
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