Chapter 3: Q. 9 (page 176)

Find the domain of $h (z) = \frac{3 z - 1}{6 z - 7}$ .

Short Answer

Expert verified

Find the domain of $\{z z \neq \frac{7}{6}\}$ .

Step by step solution

Step 1. Given information.

Find the domain of $h (z) = \frac{3 z - 1}{6 z - 7}$ .

Step 2. Find the domain.

The rational function is not defined if the denominator is equal to zero.

So,

$6 z - 7 \neq 0 6 z \neq 7 z \neq \frac{7}{6}$

So the function his defined for all real numbers, $ℝ$ , except $\frac{7}{6}$ .

The domain of the $h$ is :

$\{z z \neq \frac{7}{6}\}$ .

Step 3. Conclusion.

The domain ofhis $\{z z \neq \frac{7}{6}\}$ .

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Find the domain of $h (z) = \frac{3 z - 1}{6 z - 7}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the domain.

Step 3. Conclusion.

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Find the domain of $h (z) = \frac{3 z - 1}{6 z - 7}$ .