How do you find the domain and range of #g(x)=8/(3-7x)#?

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Answer 1 · 2017-11-20T19:07:15

The domain is #RR-{7/3}#. The range is #RR-{0}#

The denominator must be #!=0#

Therefore,

#3-7x!=0#

#7x!=3#

#x!=3/7#

So, the domain is #RR-{7/3}#

Let

#y=8/(3-7x)#

#y(3-7x)=8#

#3y-7xy=8#

#7xy=3y-8#

#x=(3y-8)/(7y)#

The same reasoning as above

#y!=0#

The range is #RR-{0}#

graph{8/(3-7x) [-12.66, 12.65, -6.33, 6.33]}