How do you find the domain and range of #g(x)=7/(7-6x)#?

1 Answer
Ratnaker Mehta
Jun 25, 2016

Domain of #g# is #RR-{7/6}.#

Range of #g# is #RR-{0}.#

Explanation:

Division by zero is not permitted, so, fun. #g# will be undefined when #7-6x=0,# i.e., when #x=7/6.#

So, Domain of #g# is #RR-{7/6}.#

Also, notice that, #AA x in RR-{7/6}, g(x)!=0,# bcz. #g(x)=0 rArr 7/(7-6x)=0 rArr 7=0,# an impossible result.

Hence, #AA x in RR-{7/6}, g(x)!=0,# meaning that the Range of #g# is #RR-{0}.#

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