What is the domain and range of #y=-3/(4x+4)#?

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Answer 1 · 2017-03-28T05:43:29

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

As you cannot divide by #0#,

#4x+4!=0#

#x!=-1#

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

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

#y=-3/(4x+4)#

#(4x+4)y=-3#

#4x+4=-3/y#

#4x=-3/y-4=-(3+4y)/(4y)#

#x=-(3+4y)/(16y)#

Therefore,

#y^-1=-(3+4x)/(16x)#

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

This is the range of #y#, that is, #R_y=RR-{0}#