# How do you find the domain and range for y=1/(x+6)?

Mar 14, 2016

Domain is all$\mathbb{R}$ except x=-6, Range is all $\mathbb{R}$ except 0
In the given function, it is quite obvious that y will have a real value for all real numbers, except x= -6 Hence domain is {x:$\mathbb{R}$, x$\ne$ -6}
To find the Range , exchange x,y and then solve for y. In the present case it would be $x = \frac{1}{y + 6}$. Solve for y, it would be $y = - 6 + \frac{1}{x}$. The domain of this function would be the range of the given function. The domain of this function is all $\mathbb{R}$ except 0. Hence the range of the given function would be all $\mathbb{R}$ except 0.