# How do you find the range for y = 1 / (x+5)?

Apr 22, 2015

$y = \frac{1}{x + 5}$

Could be written as $y \left(x + 5\right) = 1$

$\implies y x + 5 y = 1$

$\implies y x = 1 - 5 y$

$\implies x = \frac{1 - 5 y}{y}$

Now, see that the expression on the write can take all values of $y$ except $y = 0$

Conclusion: our range is $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$

OR simply written as $\mathbb{R} - \left\{0\right\}$