How do you find the domain and range for #f(x)= (x+2)/(x+7)#?

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Answer 1 · 2017-11-04T06:52:34

The domain is #x in RR-{-7}#. The range is #y in RR-{1}#

The function is #f(x)=(x+2)/(x+7)#

The denominator must be #!=0#

Therefore,

#x+7!=0#, #=>#, #x!=-7#

The domain is #x in RR-{-7}#

Let #y=(x+2)/(x+7)#

#y(x+7)=x+2#

#xy+7y=x+2#

#xy-x=2-7y#

#x(y-1)=2-7y#

#x=(2-7y)/(y-1)#

The denominator is #!=0#

#y-1!=0#, #=>#, #y!=1#

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

graph{(x+3)/(x+7) [-32.99, 24.74, -14.6, 14.27]}