Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

Question: Find $f + g$ and $f g$ for the functions f and g given in exercise 36.

Answer:

The function $f + g$ is $(f + g) (x) = x^{2} + x + 3$

$f g$ is $(f g) (x) = x^{3} + 2 x^{2} + x + 2$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1:

Composition of f and g : $(f \circ g) (a) = f (g (a))$

Step 2:

Given:

$g : ℝ \to ℝ and f : ℝ \to ℝ f (x) = x^{2} + 1 f (x) = x + 2$

Since f and g are both from $ℝ \to ℝ$ , $f \circ g and g \circ f$ are also functions from $ℝ \to ℝ$

Use the definition of composition:

$(f + g) (x) = f (x) + g (x) = (x^{2} + 1) + (x + 2) = x^{2} + x + 3 (f g) (x) = f (x) . g (x) = (x^{2} + 1) (x + 2) = x^{3} + 2 x^{2} + x + 2$

Hence, the solution is $f + g$ is $(f + g) (x) = x^{2} + x + 3$

$f g$ is $(f g) (x) = x^{3} + 2 x^{2} + x + 2$

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Discrete Mathematics and its Applications

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Question: Find $f + g$ and $f g$ for the functions f and g given in exercise 36.

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Discrete Mathematics and its Applications

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Question: Find f + g and fg for the functions f and g given in exercise 36.

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Question: Find $f + g$ and $f g$ for the functions f and g given in exercise 36.