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Q. 6

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Precalculus Enhanced with Graphing Utilities

Found in: Page 256

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

True or False. The domain of the composite function $(f \circ g) (x)$ is the same as the domain of $g (x)$ .

This statement is true.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The domain of the composite function $(f \circ g) (x)$ is the same as the domain of $g (x)$ .

Step 2. Domain of a composite function.

The function $f (g (x)) = (f \circ g) (x)$

$\Rightarrow f (g (x)) = g (x)$ .

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For an exponential function, $f (x) = C a^{x}, \frac{f (x + 1)}{f (x)} =$

If $f (x) = a^{x}$ , show that $f (A + B) = f (A) . f (B)$ .

Vehicle Stopping Distance Taking into account reaction time, the distance $d$ (in feet) that a car requires to come to a complete stop while traveling $r$ miles per hour is given by the function

localid="1646198784356" $d (r) = 6.97 r - 90.39$

a. Express the speed $r$ at which the car is traveling as a function of the distance localid="1646198792401" $d$ required to come to a complete stop

b. Verify that localid="1646198797631" $r = r (d)$ is the inverse of localid="1646198802104" $d = d (r)$ by showing that localid="1646198806352" $r (d (r)) = r$ and localid="1646198811055" $d (r (d)) = d$

c. Predict the speed that a car was traveling if the distance required to stop was localid="1646198818232" $300$ feet.

$d (r (d)) = d$

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = 7 - 3 e^{2 x}$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

True or False. The domain of the composite function $(f \circ g) (x)$ is the same as the domain of $g (x)$ .

Step by Step Solution

Step 1. Given Information.

Step 2. Domain of a composite function.

Most popular questions for Math Textbooks

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

True or False. The domain of the composite function f∘gx is the same as the domain of g(x).

Step by Step Solution

Step 1. Given Information.

Step 2. Domain of a composite function.

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True or False. The domain of the composite function $(f \circ g) (x)$ is the same as the domain of $g (x)$ .