How do you find the domain and range of #g(x) = -11/(4 + x)#?

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Answer 1 · 2018-07-17T07:52:10

The domain is #x in (-oo,4)uu(4,+oo)#. The range is #y in (-oo,0)uu(0,+oo)#

The function is

#f(x)=-11/(4+x)#

The denominator must be #!=0#

Therefore,

#4+x!=0#

#x!=-4#

The domain is #x in (-oo,4)uu(4,+oo)#

To find the domain, Let

#y=-11/(4+x)#

#y(4+x)=-11#

#yx+4y=-11#

#yx=-11-4y#

#x=(-11-4y)/y#

The denominator must be #!=0#

#y!=0#

The range is #y in (-oo,0)uu(0,+oo)#

graph{-11/(4+x) [-33.13, 18.18, -13.24, 12.43]}