In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using y = f ( x ) to represent a function, an applied problem might use C = C ( q ) to represent the cost C of manufacturing q units of a good. Because of this, the inverse notation f − 1 used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as C = C ( q ) will be q = q ( C ) . So C = C ( q ) is a function that represents the cost C as a function of the number q of units manufactured, and q = q ( C ) is a function that represents the number q as a function of the cost C . Problems 91-94 illustrate this idea. Temperature Conversion The function F ( C ) = 9 5 C + 32 converts a temperature from C degrees Celsius to F degrees Fahrenheit. (a) Express the temperature in degrees Celsius C as a function of the temperature in degrees Fahrenheit F . (b) Verify that C = C ( F ) is the inverse of F = F ( C ) by showing that C ( F ( C ) ) = C and F ( C ( F ) ) = F . (c) What is the temperature in degrees Celsius if it is 70 degrees Fahrenheit?
In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using y = f ( x ) to represent a function, an applied problem might use C = C ( q ) to represent the cost C of manufacturing q units of a good. Because of this, the inverse notation f − 1 used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as C = C ( q ) will be q = q ( C ) . So C = C ( q ) is a function that represents the cost C as a function of the number q of units manufactured, and q = q ( C ) is a function that represents the number q as a function of the cost C . Problems 91-94 illustrate this idea. Temperature Conversion The function F ( C ) = 9 5 C + 32 converts a temperature from C degrees Celsius to F degrees Fahrenheit. (a) Express the temperature in degrees Celsius C as a function of the temperature in degrees Fahrenheit F . (b) Verify that C = C ( F ) is the inverse of F = F ( C ) by showing that C ( F ( C ) ) = C and F ( C ( F ) ) = F . (c) What is the temperature in degrees Celsius if it is 70 degrees Fahrenheit?
Solution Summary: The author explains how the function F converts a temperature from C degrees Celsius to F degrees Fahrenheit.
In applications, the symbols used for the independent and dependent variables are often based on common usage. So, rather than using
to represent a function, an applied problem might use
to represent the cost
of manufacturing q units of a good. Because of this, the inverse notation
used in a pure mathematics problem is not used when finding inverses of applied problems. Rather, the inverse of a function such as
will be
. So
is a function that represents the cost
as a function of the number
of units manufactured, and
is a function that represents the number
as a function of the cost
. Problems 91-94 illustrate this idea.
Temperature Conversion The function
converts a temperature from
degrees Celsius to
degrees Fahrenheit.
(a) Express the temperature in degrees Celsius
as a function of the temperature in degrees Fahrenheit
.
(b) Verify that
is the inverse of
by showing that
and
.
(c) What is the temperature in degrees Celsius if it is 70 degrees Fahrenheit?
If the point in function f(x) has the coordinates (-2, 4), then what would be the coordinate for that point in the inverse of f(x)?
I am not sure I am understanding the one-to-one part. If the functions are equal to one another, wouldn't that mean that they aren't one-to-one
In a cutting-edge greenhouse, an advanced climate digital control system is installed based on a DC inverter that maintains the desired temperature in the green house. The system's temperature control function is described by
where T represents the temperature inside the greenhouse in degrees Celsius, and C represents the desired control setting on the climate control system of DC inverter.
Based on that information, please provide answers to the following questions:
(i) Using the concept of the inverse function, determine the control setting (C) as a function of greenhouse temperature (T). Please outline all the steps clearly.
(ii)Discuss any practical limitations or considerations that may impact the functionality of the inverse function within the context of the greenhouse climate control system.
Chapter 5 Solutions
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY