Chapter 5: Q 42. (page 298)

Find the domain of the function.
$g (x) = 8 + 5 \ln (2 x + 3)$

Short Answer

Expert verified

The domain of the given function $g (x)$ is $(- \frac{3}{2}, \infty)$ .

Step by step solution

Step 1. Given information

A logarithmic function is given as $g (x) = 8 + 5 \ln (2 x + 3)$

Step 2. Formula Used

The domain of the logarithmic function $f (x) = \ln (x)$ is determined by $x > 0$ .

Step 3. Finding The Domain

The function is $g (x) = 8 + 5 \ln (2 x + 3)$

Now, for the domain,

$2 x + 3 > 0$

On solving

$2 x > - 3 x > - \frac{3}{2}$

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

interval notation, is $(- \frac{3}{2}, \infty)$ .

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Find the domain of the function.
$g (x) = 8 + 5 \ln (2 x + 3)$

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.gx=8+5ln2x+3

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.
$g (x) = 8 + 5 \ln (2 x + 3)$