Question

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

Short answer

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

Step-by-step solution

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