How do you find the domain and range for #y = 2/(x-1)#?

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Answer 1 · 2017-02-25T11:10:36

The domain of #y# is #D_y=RR-{1}#
The range of #y# is #R_y=RR-{0}#

As you cannot divide by #0#, #x!=1#

The domain of #y# is #D_y=RR-{1}#

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

#y=2/(x-1)#

#(x-1)y=2#

#xy-y=2#

#xy=y+2#

#x=(y+2)/y#

Therefore,

#y^-1=(x+2)/x#

The domain of #y^-1=RR-{0}#

This is the range of #y#

The range of #y# is #R_y=RR-{0}#