Explanation Formula used: The addition of two functions is given below, ( f + g ) ( x ) = f ( x ) + g ( x ) . (1) The subtraction of two functions is given below, ( f − g ) ( x ) = f ( x ) − g ( x ) . (2) The multiplication of two functions is given below, f g ( x ) = f ( x ) g ( x ) . (3) The quotient of two functions is given below, f g ( x ) = f ( x ) g ( x ) . (4) Where, g ( x ) ≠ 0 . The given functions are, f ( x ) = x 2 + 2 x g ( x ) = 3 x 2 − 1 Substitute x 2 + 2 x for f ( x ) and 3 x 2 − 1 for g ( x ) in equation (1), to find the value of the function f + g , ( f + g ) ( x ) = ( x 2 + 2 x ) + ( 3 x 2 − 1 ) = 4 x 2 + 2 x − 1 The domain is the set of all possible inputs for a function. The function ( f + g ) ( x ) = 4 x 2 + 2 x − 1 is defined for every real number, therefore the domain of the function ( f + g ) ( x ) = 4 x 2 + 2 x − 1 is set of all real numbers ℝ . Domain of ( f + g ) = { x | x ∈ ℝ } It is also written in interval notation as given below, ( − ∞ , ∞ ) Substitute x 2 + 2 x for f ( x ) and 3 x 2 − 1 for g ( x ) in equation (2), to find the value of the function f − g , ( f − g ) ( x ) = ( x 2 + 2 x ) − ( 3 x 2 − 1 ) = x 2 + 2 x − 3 x 2 + 1 = − 2 x 2 + 2 x + 1 The domain is the set of all possible inputs for a function. The function ( f − g ) ( x ) = − 2 x 2 + 2 x + 1 is defined for every real number, therefore the domain of the function ( f − g ) ( x ) = − 2 x 2 + 2 x + 1 is set of all real numbers ℝ . Domain of ( f − g ) = { x | x ∈ ℝ } It is also written in interval notation as given below, ( − ∞ , ∞ ) Substitute x 2 + 2 x for f ( x ) and 3 x 2 − 1 for g ( x ) in equation (3), to find the value of the function f g , ( f g ) ( x ) = ( x 2 + 2 x ) ( 3 x 2 − 1 ) = 3 x 4 − x 2 + 6 x 3 − 2 x = 3 x 4 + 6 x 3 − x 2 − 2 x The domain is the set of all possible inputs for a function

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ISBN: 9781305537163

Author: Stewart

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Chapter 2.7, Problem 12E

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To evaluate: The values of f+g , f−g , fg and fg and to find their domains.

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Chapter 2.7, Problem 11E

Chapter 2.7, Problem 13E

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Chapter 2 Solutions

EBK PRECALCULUS MATH.FOR CALCULUS

Ch. 2.1 - If f(x) = x3 + 1, then (a) the value of f at x = 1...Ch. 2.1 - For a function f, the set of all possible inputs...Ch. 2.1 - (a) Which of the following functions have 5 in...Ch. 2.1 - A function is given algebraically by the formula...Ch. 2.1 - A function f is a rule that assigns to each...Ch. 2.1 - Yes or No? If No, give a reason. Let f be a...Ch. 2.1 - Function Notation Express the rule in function...Ch. 2.1 - Function Notation Express the rule in function...Ch. 2.1 - Function Notation Express the rule in function...Ch. 2.1 - Function Notation Express the rule in function...

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The values of f + g , f − g , f g and f g and to find their domains.

Solution Summary: The author evaluates the values of f+g, and respectively, and to find their domains.

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To evaluate: The values of f+g , f−g , fg and fg and to find their domains.

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Chapter 2 Solutions