Chapter 5: Q 41. (page 298)

Find the domain of the function.
$f (x) = 3 - 2 \log_{4} (\frac{x}{2} - 5)$

Short Answer

Expert verified

The domain of the given function $f (x)$ is $(10, \infty)$ .

Step by step solution

Step 1. Given information

A logarithmic function is given as $f (x) = 3 - 2 \log_{4} (\frac{x}{2} - 5)$

Step 2. Formula Used

The domain of the logarithmic function $f (x) = \log_{a} (x)$ is determined by $x > 0$ .

Step 3. Finding The Domain

The function is $f (x) = 3 - 2 \log_{4} (\frac{x}{2} - 5)$

Now, for the domain,

$\frac{x}{2} - 5 > 0$

On solving

$x - 10 > 0 x > 10$

The required domain of $f (x)$ , using

interval notation, is $(10, \infty)$ .

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Find the domain of the function.
$f (x) = 3 - 2 \log_{4} (\frac{x}{2} - 5)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Formula Used

Step 3. Finding The Domain

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Find the domain of the function.
$f (x) = 3 - 2 \log_{4} (\frac{x}{2} - 5)$