Explanation Given information: f ( x ) = 2 3 x + 2 , g ( x ) = 3 2 x + 3 Concept Used: Let f and g are the functions with domain D 1 and D 2 respectively, and range D 2 and D 1 respectively. Then these functions are inverses of each other if g [ f ( x ) ] = x for all x in D 1 And f [ g ( x ) ] = x for all x in D 2 Calculation: In order to determine if the functions f ( x ) = 2 3 x + 2 , g ( x ) = 3 2 x + 3 are inverses of each other

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 1.5, Problem 4PS

To determine

To find if the functions

f(x)=23x+2,g(x)=32x+3

are inverses of each other

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Chapter 1.5, Problem 3PS

Chapter 1.5, Problem 5PS

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(a) Write the equation of a function which fits each of the tables below. (b) Show and explain how you determined the function from the table. x f(x) -1 1 0 -1.5 1 -4 2 -6.5 3 -9 x g(x) -1 0.5 0 2 1 8 2 32 3 128 c) Let g^−1 be the inverse function of g from problem 2. Make a table of values for the function g^−1.

What patterns are shown in this problem and describe whether these patterns can be generalized to all functions and their inverses.

What patterns are shown between the two equations and describe whether these patterns can be generalized to all functions and inverses.

Chapter 1 Solutions

Calculus

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To find if the functions f ( x ) = 2 3 x + 2 , g ( x ) = 3 2 x + 3 are inverses of each other

Solution Summary: The author explains that the functions f and g are not inverses of each other.

Concept explainers

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To find if the functions

f(x)=23x+2,g(x)=32x+3

are inverses of each other

Want to see the full answer?

Chapter 1 Solutions

To find if the functions f ( x ) = 2 3 x + 2 , g ( x ) = 3 2 x + 3 are inverses of each other

Solution Summary: The author explains that the functions f and g are not inverses of each other.

Concept explainers

Videos

To find if the functions f(x)=23x+2,g(x)=32x+3 are inverses of each other

Want to see the full answer?

Chapter 1 Solutions

To find if the functions

f(x)=23x+2,g(x)=32x+3

are inverses of each other