# What is the range of the function f(x) = 7 / (2x-10)?

Aug 24, 2017

$y \in \mathbb{R} , y \ne 0$

#### Explanation:

$\text{given } y = \frac{7}{2 x - 10}$

$\text{rearrange making x the subject}$

$\Rightarrow y \left(2 x - 10\right) = 7 \leftarrow \textcolor{b l u e}{\text{cross-multiplying}}$

$\Rightarrow 2 y x - 10 y = 7$

$\Rightarrow 2 y x = 7 + 10 y$

$\Rightarrow x = \frac{7 + 10 y}{2 y}$

$\text{the denominator cannot equal zero}$

$2 y = 0 \Rightarrow y = 0 \leftarrow \textcolor{red}{\text{ is excluded value}}$

$\Rightarrow \text{range is } y \in \mathbb{R} , y \ne 0$
graph{7/(2x-10) [-10, 10, -5, 5]}