What is the domain and range of #y=(x^2 -5x -6) / (x^2 -3x -18)#?

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Answer 1 · 2018-03-17T23:23:41

The domain of the function is #x in RR-{-3}#. The range is #y in RR-{1}#

Factorise the numerator and denominator

#y=(x^2-5x-6)/(x^2-3x-18)=((x+1)cancel(x-6))/((x+3)cancel(x-6))#

#=(x+1)/(x+3)#

The denominator is #!=0#, therefore

#x+3!=0#, #=>#, #x!=-3#

The domain of the function is ##x in RR-{-3}

To determine the range, proceed as follows

#y=(x+1)/(x+3)#

#y(x+3)=x+1#

#yx-x=1-3y#

#x(y-1)=1-3y#

#x=(1-3y)/(y-1)#

The denominator is #!=0#

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

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

graph{(x^2-5x-6)/(x^2-3x-18) [-16.02, 16.02, -8.01, 8.01]}