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Q. 120

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Precalculus Enhanced with Graphing Utilities

Found in: Page 287

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

If $f (x) = a^{x}$ , show that $f (- x) = \frac{1}{f (x)}$ .

To prove $f (- x) = \frac{1}{f (x)}$ , first find $f (- x)$ and apply the laws of exponents.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Consider the given question, $f (x) = a^{x} f (- x) = \frac{1}{f (x)}$

Then,

$f (- x) = a^{- x}$

Step 2. Use the law of exponents.

Using laws of exponents, $m^{- n} = \frac{1}{m^{n}}$ ,

$f (- x) = \frac{1}{a^{x}} f (- x) = \frac{1}{f (x)}$

Therefore, $L H S = R H S$ .

Hence, proved.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

If $f (x) = a^{x}$ , show that $f (- x) = \frac{1}{f (x)}$ .

Step by Step Solution

Step 1. Given information.

Step 2. Use the law of exponents.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

If fx=ax, show that f-x=1fx.

Step by Step Solution

Step 1. Given information.

Step 2. Use the law of exponents.

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If $f (x) = a^{x}$ , show that $f (- x) = \frac{1}{f (x)}$ .