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

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Answer 1 · 2017-01-31T11:10:23

The domain is # RR-{0}#
The range is #RR-{3}#

As you cannot divide by #0#, #=>#, #x!=0#

The domain of #y# is #RR-{0}#

To find the range, we need to calculate #y^-1#

The domain of #y^-1# is the range

#y=3(x-2)/x#

#yx=3x-6#

#3x-yx=6#

#x(3-y)=6#

#x=6/(3-y)#

Therefore,

#y^-1=6/(3-x)#

As you cannot divide by #0#, #=>#, #x!=3#

The range is #RR-{3}#

graph{(y-(3x-6)/x)(y-3)(y-100x)=0 [-25.65, 25.65, -12.83, 12.82]}