What is the domain and range of #g(x) = (7x+4)/(x+4)#?

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Answer 1 · 2018-04-29T12:59:17

The domain is #x in (-oo, -4)uu (-4, +oo)#.
The range is #y in (-oo, 7) uu (7, +oo)#

Let #y=(7x+4)/(x+4)#

The denominator is #!=0#

Therefore,

#x+4!=0#

#x!=-4#

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

Also,

#y(x+4)=7x+4#

#yx+4y=7x+4#

#yx-7x=4-4y#

#x(y-7)=(4-4y)#

#x=(4-4y)/(y-7)#

The denominator is #!=0#

Therefore

#y-7!=0#

#y!=7#

The range is #y in (-oo, 7) uu (7, +oo)#

graph{(y-((7x+4)/(x+4)))(y-7)=0 [-36.53, 36.52, -18.28, 18.27]}