Question

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

Answer 1

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.