Q. 9 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

Find the domain of $\left\{\overline{)z}z\ne \frac{7}{6}\right\}$.

Step 1. Given information.

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

Step 2. Find the domain.

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

So,

$$\begin{gathered} 6z-7\ne 0 \\ 6z\ne 7 \\ z\ne \frac{7}{6} \end{gathered}$$

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

The domain of the $h$ is :

$\left\{\overline{)z}z\ne \frac{7}{6}\right\}$.

Step 3. Conclusion.

The domain of h is $\left\{\overline{)z}z\ne \frac{7}{6}\right\}$.