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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 107. (page 309)

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

Short Answer

Expert verified

The result is shown in the explanation.

Step by step solution

Step 1. Given information.

Consider the given function.

$f (x) = \log_{a} x$

Step 2. Calculation.

Substitute $\frac{1}{x}$ for x in the given function.

$\begin{array}{rcl} f (\frac{1}{x}) & = & \log_{a} (\frac{1}{x}) \\ = & \log_{a} 1 - \log_{a} x \\ = & 0 - \log_{a} x \\ = & - \log_{a} x \end{array}$

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If fx=logax, show thatf1x=-fx.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

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