# What is the domain and range of F(x) = 7/(6x-5)?

Sep 8, 2015

Domain: $x \in \mathbb{R} , x \ne \frac{5}{6}$
Range: $F \left(x\right) \in \mathbb{R} , F \left(x\right) \ne 0$

#### Explanation:

$F \left(x\right) = \frac{7}{6 x - 5}$ is not defined if $\left(6 x - 5\right) = 0$ (i.e. if $x = \frac{5}{6}$

therefore $x = \frac{5}{6}$ must be excluded from the Domain

Consider the partial inverse equation:
$F \left(x\right) = \frac{7}{6 x - 5}$
$\rightarrow 6 x - 5 = \frac{7}{F} \left(x\right)$

This will not be defined if (F(x)=0
therefore $F \left(x\right) = 0$ must be excluded from the range.
graph{7/(6x-5) [-20.27, 20.26, -10.13, 10.15]}