Explanation Given information: The functions, F ( x ) = x 2 + 1 and G ( x ) = x + 1 . Formula used: The addition of the functions f and g is represented as f + g , mathematically it is denoted by, ( f + g ) ( x ) = f ( x ) + g ( x ) Graphically the height of addition of two functions is the addition of individual height of the function that is height of first function added to height of second function. Calculation: Consider the provided functions, F ( x ) = x 2 + 1 and G ( x ) = x + 1 . Recall the addition of the functions f and g is represented as f + g , mathematically it is denoted by, ( f + g ) ( x ) = f ( x ) + g ( x ) Evaluate the value of f ( x ) + g ( x ) that is sum of the functions, F ( x ) + G ( x ) = x 2 + 1 + x + 1 Group the like terms, F ( x ) + G ( x ) = x 2 + 1 + x + 1 = x 2 + x + 1 + 1 Combine the like terms, F ( x ) + G ( x ) = x 2 + 1 + x + 1 = x 2 + x + 1 + 1 = x 2 + x + 2 Therefore, the value of sum of the function is x 2 + x + 2 . Now, evaluate the value of the individual function F ( x ) = x 2 + 1 , G ( x ) = x + 1 and sum of the function, F ( x ) + G ( x ) = x 2 + x + 2 at the provided points x = − 2 , x = − 1 , x = 0 , x = 1 and x = 2 . For x = − 2 , substitute the value of x in the functions, F ( x ) = x 2 + 1 , G ( x ) = x + 1 and F ( x ) + G ( x ) = x 2 + x + 2 . F ( − 2 ) = ( − 2 ) 2 + 1 = 4 + 1 = 5 Next, G ( − 2 ) = − 2 + 1 = − 1 Last, F ( − 2 ) + G ( − 2 ) = ( − 2 ) 2 − 2 + 2 = 4 For x = − 1 , substitute the value of x in the functions, F ( x ) = x 2 + 1 , G ( x ) = x + 1 and F ( x ) + G ( x ) = x 2 + x + 2 . F ( − 1 ) = ( − 1 ) 2 + 1 = 1 + 1 = 2 Next, G ( − 1 ) = − 1 + 1 = 0 Last, F ( − 1 ) + G ( − 1 ) = ( − 1 ) 2 − 1 + 2 = 2 For x = 0 , substitute the value of x in the functions, F ( x ) = x 2 + 1 , G ( x ) = x + 1 and F ( x ) + G ( x ) = x 2 + x + 2

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

3rd Edition

ISBN: 9780840064189

Author: Frederick R. Adler

Publisher: Cengage Learning

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Chapter 1.2, Problem 19E

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To calculate: the values for the sum of the functions F(x)=x2+1 and G(x)=x+1 , at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their sum.

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Chapter 1.2, Problem 18E

Chapter 1.2, Problem 20E

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For each of the following sums of functions, graph each component piece. Compute the values at x =−2, x =−1, x = 0, x = 1, and x = 2 and plot the sum. F(x) = x² + 1 and H(x) =−x + 1.

Chapter 1 Solutions

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

Ch. 1.2 - Identify the variables and parameters in the...Ch. 1.2 - Prob. 2E Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Compute the values of the following functions at...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...Ch. 1.2 - Graph the given points and say which point does...

Ch. 1.2 - Evaluate the following functions at the given...Ch. 1.2 - Evaluate the following functions at the given...Ch. 1.2 - Prob. 13E Ch. 1.2 - Prob. 14E Ch. 1.2 - Prob. 15E Ch. 1.2 - Prob. 16E Ch. 1.2 - Prob. 17E Ch. 1.2 - Prob. 18E Ch. 1.2 - Prob. 19E Ch. 1.2 - Prob. 20E Ch. 1.2 - Prob. 21E Ch. 1.2 - Prob. 22E Ch. 1.2 - Prob. 23E Ch. 1.2 - Prob. 24E Ch. 1.2 - Prob. 25E Ch. 1.2 - Find the inverses of each of the following...Ch. 1.2 - Prob. 27E Ch. 1.2 - Prob. 28E Ch. 1.2 - Prob. 29E Ch. 1.2 - Graph each of the following functions and its...Ch. 1.2 - Graph each of the following functions and its...Ch. 1.2 - Graph each of the following functions and its...Ch. 1.2 - Prob. 33E Ch. 1.2 - Find the compositions of the given functions....Ch. 1.2 - Prob. 35E Ch. 1.2 - Prob. 36E Ch. 1.2 - Prob. 37E Ch. 1.2 - Prob. 38E Ch. 1.2 - Prob. 39E Ch. 1.2 - Prob. 40E Ch. 1.2 - Prob. 41E Ch. 1.2 - Prob. 42E Ch. 1.2 - Prob. 43E Ch. 1.2 - Prob. 44E Ch. 1.2 - Prob. 45E Ch. 1.2 - Prob. 46E Ch. 1.2 - Prob. 47E Ch. 1.2 - Prob. 48E Ch. 1.2 - Prob. 49E Ch. 1.2 - Prob. 50E Ch. 1.2 - Prob. 51E Ch. 1.2 - Prob. 52E Ch. 1.2 - The following series of functional compositions...Ch. 1.2 - The following series of functional compositions...Ch. 1.2 - The following series of functional compositions...Ch. 1.2 - Prob. 56E Ch. 1.2 - Prob. 57E Ch. 1.2 - Prob. 58E Ch. 1.2 - Prob. 59E Ch. 1.2 - Prob. 60E Ch. 1.2 - Prob. 61E Ch. 1.2 - Prob. 62E Ch. 1.2 - Prob. 63E Ch. 1.2 - Prob. 64E Ch. 1.2 - Prob. 65E Ch. 1.2 - Prob. 66E Ch. 1.2 - Prob. 67E Ch. 1.2 - Prob. 68E Ch. 1.2 - Prob. 69E Ch. 1.2 - Prob. 70E Ch. 1.3 - Prob. 1E Ch. 1.3 - Prob. 2E Ch. 1.3 - Prob. 3E Ch. 1.3 - Prob. 4E Ch. 1.3 - Prob. 5E Ch. 1.3 - Prob. 6E Ch. 1.3 - Prob. 7E Ch. 1.3 - Prob. 8E Ch. 1.3 - Prob. 9E Ch. 1.3 - Prob. 10E Ch. 1.3 - Prob. 11E Ch. 1.3 - Prob. 12E Ch. 1.3 - Prob. 13E Ch. 1.3 - Prob. 14E Ch. 1.3 - Prob. 15E Ch. 1.3 - Prob. 16E Ch. 1.3 - Prob. 17E Ch. 1.3 - Prob. 18E Ch. 1.3 - Prob. 19E Ch. 1.3 - Prob. 20E Ch. 1.3 - Prob. 21E Ch. 1.3 - Prob. 22E Ch. 1.3 - 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the values for the sum of the functions F ( x ) = x 2 + 1 and G ( x ) = x + 1 , at x = − 2 , x = − 1 , x = 0 , x = 1 and x = 2 , graph component piece functions and their sum.

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To calculate: the values for the sum of the functions F(x)=x2+1 and G(x)=x+1 , at x=−2,x=−1,x=0,x=1 and x=2 , graph component piece functions and their sum.

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Chapter 1 Solutions