How do you find the domain and range of # f(x) = (x+6 )/ (2x+1 )#?

1 Answer
Monzur R.
Jul 18, 2017

#f:RR rarr RR, x != -1/2#

Explanation:

To find which values of #x# don't belong to the domain of #f#, we have to set the denominator of #f=0# and solve for #x#

#2x+1=0#

#x=-1/2#

Therefore, #-1/2# is the only invalid real in the domain. Also, since #x=-1/2# is an asymptote, we know that #f# will increase with bound towards #+-oo#. Therefore, #f# maps to all #y in RR#.

Combining these two, we can define

#f:RR rarr RR#

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