What is the domain and range of #f(x) = (x+6 )/ (2x+1) #?

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Answer 1 · 2018-01-16T10:13:57

The domain is # x in RR-{-1/2}#.
The range is #y in RR-{1/2}#

As you cannot divide by #0#, the denominator is #!=0#

Therefore,

#2x+1!=0#

#=>#, #x"=-1/2#

The domain is # x in RR-{-1/2}#

In order to find the range, proceed as follows .

Let #y=(x+6)/(2x+1)#

#y(2x+1)=x+6#

#2xy+y=x+6#

#2xy-x=6-y#

#x(2y-1)=(6-y)#

#x=(6-y)/(2y-1)#

In order for #x# to have solutions,

#2y-1!=0#

#y!=1/2#

The range is #y in RR-{1/2}#

graph{(x+6)/(2x+1) [-18.02, 18.01, -9.01, 9.01]}