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

1 Answer
Mar 14, 2016

Answer:

Domain is all#RR# except x=-6, Range is all #RR# except 0

Explanation:

Domain of a function of x, expressed as f(x) or more commonly as y, is that set of real numbers(x), for which f(x) has a real value.

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:#RR#, x#!=# -6}

To find the Range , exchange x,y and then solve for y. In the present case it would be #x= 1/(y+6)#. Solve for y, it would be #y= -6+1/x#. The domain of this function would be the range of the given function. The domain of this function is all #RR# except 0. Hence the range of the given function would be all #RR# except 0.