# How do you find the domain and range of g(x)=7/(7-6x)?

Jun 25, 2016

Domain of $g$ is $\mathbb{R} - \left\{\frac{7}{6}\right\} .$

Range of $g$ is $\mathbb{R} - \left\{0\right\} .$

#### Explanation:

Division by zero is not permitted, so, fun. $g$ will be undefined when $7 - 6 x = 0 ,$ i.e., when $x = \frac{7}{6.}$

So, Domain of $g$ is $\mathbb{R} - \left\{\frac{7}{6}\right\} .$

Also, notice that, $\forall x \in \mathbb{R} - \left\{\frac{7}{6}\right\} , g \left(x\right) \ne 0 ,$ bcz. $g \left(x\right) = 0 \Rightarrow \frac{7}{7 - 6 x} = 0 \Rightarrow 7 = 0 ,$ an impossible result.

Hence, $\forall x \in \mathbb{R} - \left\{\frac{7}{6}\right\} , g \left(x\right) \ne 0 ,$ meaning that the Range of $g$ is $\mathbb{R} - \left\{0\right\} .$